Monday, 26 June 2017

S9.309 - Tile And Error


It's the first "math-tan" to be associated with another subject, with my thanks to John's remark last week. The design was based on how there's only 3 tessellations with regular polygons (triangles, squares and hexagons), with a Schlafli symbol tossed in for good measure. There's an online tessellation artist at that link if you want to play around.

As an alternative link, the sign in the Connecticut deli asking to refrain from mathematics discussion has been explained.

<<FIRST <LAST WK INDEX NEXT WK> END>>

SIGNUM: Picking up an automated transmission.
QLOGAN: On screen.
SIGNUM: Ice cream?
PARA: I’ll put it up.
TESSIE (on viewer): Hiyo, Tessie Layshun here! Come to Art for all your tiling needs.
TESSIE (on viewer): We can Escher you right in, so keep us in your pattern buffer. Our ad is on the regional bulletin board. ... Hiyo, Tessie-- *click*
QLOGAN: Hmm, opinions?
SLOPE: I could go for some ice cream.

Monday, 19 June 2017

S9.308 - Scan Dull



The gazebo's back, slightly redesigned so it's easier to draw. It was last seen on the mission QLogan's referring to (from 2015!) "88 mph". The "Beta Group" Para references is from the serial days, the original subject exploration. (It's a searchable term, if you only want to see their entries.) Now, to be fair here, Maud's failure may not have been due to the staffing.

In math news, apparently last Saturday (June 17) was the second annual World Tessellation Day. Yay?

<<FIRST <LAST WK INDEX NEXT WK> END>>

(External shot of Gazebo/Logan's Ship)
PARA: QLogan, how exactly did you pick your crew for this subject exploration?
(Internal to the Ship)
QLOGAN: I scanned old records.
PARA: You mean for the beta group?
QLOGAN: No, for sending Maud back in time.
NIS: As head of science, I say you can’t add a magical switch!
HYPER: As chief engineer I say I can!
QCSC: You two want a trip to my brig?!
PARA: You know Maud’s mission failed, yeah?
QLOGAN: I wasn’t scanning that closely.

Monday, 12 June 2017

S9.307 - Tourism de Force



That mouse rollover text has been an idea for over a year, that I haven't used. Incidentally, it's true that more numbers are irrational than natural - there are levels of infinity. There's the same number of fractions as there are integers though.

Unrelated, apparently for this Council meeting arc (that started a couple weeks back) some characters took off their earrings. I have no excuse.

<<FIRST <LAST WK INDEX NEXT WK> END>>

EXPONA: Having a casino would help with tourism.
PARA: Casinos aren’t fair. Let’s have a fair, and ferris wheel!
VERSINE: No, an escape room. To trap people here.
ARCTAN: Let’s create the curriculum’s biggest something.
QROOT: Biggest fights?
ARCTAN: No.
GAMMA: Could we use a healthy slogan? Like ‘Our numbers are all natural.’
QHYPER: More numbers are irrational than natural!
QLOGAN: I’ll go recruit, then see what other subjects are up to.
QSINE: Should we somehow consult TPTB?
QCOTAN: A tourism pamphlet can have math models.
QLYN: Right...
QCOTAN: Math swimsuit models.
QLYN: No.

Monday, 5 June 2017

S9.306 - Side Kicks



In the absence of suggestions, that's what we get. It's not quite retroactive continuity, I've been careful not to show that part of the table, and why else would the others all sit on the same side?

If you have tourism ideas to bring other subjects into math, the field is still open, as the buffer is empty again.

<<FIRST <LAST WK INDEX NEXT WK> END>>

QSINE: Tourism won the vote. We’ll need a minister of transport, so I chose QLogan, as he has inherited the gazebo ship.
QROOT: As education minister, I must ask if he has the same qualifications as his former serial counterpart.
 (One side of the room stares)
VERSINE: Since when are you a minister?
QROOT: Since the start. Pay attention to this side of the table.
QCOTAN: I keep forgetting to come to meetings.

Monday, 29 May 2017

S9.305 - Be Trade



Got any thoughts of subjects to bring in? (I know, I never learned my lesson from Series 4.) Or anything touristy? Also, last chance for anyone to suggest a new minister for the Council Table. Environment and Education will be filled one way or another.

Meanwhile, there was another Art Aside last Thursday, if you missed it.

<<FIRST <LAST WK INDEX NEXT WK> END>>

QSINE: We should contact the other subjects. We'll need materials to fix the Jump Gate.
VERSINE: Time for a raid! I’ll recruit. QLyn, how many phasers are available?
GAMMA: Or, we make math a better tourist spot. Other subjects visit, and we can open trade.
QHYPER: Oh, sure. We’ve been sooo good at publicity.
PARA: Can’t you be more positive?
QHYPER: Do I look like an ellipse?

Thursday, 25 May 2017

S9.304b - Art Aside: Sine

The end of every month is becoming a bit of an Art Showcase. To end February there was a Hyper FanArt, to end March there was Expona Commissioned Art and to end April I was dealing with the Series Bible. (I still may, at some point, get around to doing new images for the fractals.) So, as it's the last Thursday of May, here is the President of Mathematics, Sine.


Sine by Tannistha (May 2016)

That commission is from Anime North last year (2016). (Tannistha mailed it to me after the con.) She'll be at Table F08 at Anime North this coming weekend, so if you're in the area, maybe check her out. (I'll be around the convention too this weekend, though I haven't really decided on commissions yet.) Note that's a full version of the image I used for Sine's podium way back in "Word Choice".

It's also worth mentioning here that John Golden sent me more fan art for my birthday last month, namely Maud, Rhys, Root and Expona head shots. I'm keeping that one to myself for now, though will mention I kind of love how Expona's hair covers one of her eyes, that's a fun look for her. Also in April, I got a rough sketch of Hyper by the creator of "Astria Legends", a comic which has colour personified angels. Consider checking that out too.

That's all for now, new comic Monday! Feel free to comment (I changed the header art, does that work?), send some art in, or simply sketch your own versions of math at home. I am, as has been said, a pretty niche market, but if any of this inspires you towards math (or comics), that makes me happy. Thanks for reading.

Monday, 22 May 2017

S9.304 - Reciprocatings Aw



Rhys is, of course, RhysPlus for a=0. Not sure about keeping Logan's eyepatch on the new Reci. Thoughts?

<<FIRST <LAST WK INDEX NEXT WK> END>>

RHYSPLUS: Cool new threads. Now let’s see how my “a” value works.
RHYS: Before, I was a special form of Hyper. Now I’m a special form of RhysPlus. I can’t win.
RECI: You’re female now. At least that’s different.
RHYS: Probably means I’m destined to marry him.
RECI: You think? Because maybe I marry RhysPlus first.
RHYS: Your iPatch seems to be giving you a superiority complex.

Monday, 15 May 2017

S9.303 - Secant Touch This



You probably need this explanation for that very old reference.

Meanwhile, Rev. Fitz has been checking out new serials every day this month, including the start of Taylor’s Polynomials (from back in 2011). You can read his analysis here. He also runs a comic called “Mr. Square”, check that out here.

<<FIRST <LAST WK INDEX NEXT WK> END>>

TANGENT: Becoming Secant unnerved me. I’m going to stay as Slope for the moment. Away from trig.
QSINE: I understand.
QTAN: (grabs Tan) Everyone else has had more sec(x) than me!
QTAN: (grabs Para) Does anyone else get that feeling?
PARA: ?
QTAN (off panel): Does everyone - does everyone - does everyone think -
QSINE: Pardon our Tangent.

Monday, 8 May 2017

S9.302 - Sixth Sense



Para got to decide because she's Minister of Justice. This may be the first time I've indicated that degree number is tied to figure/bustline (like memory for the original OS-tans). Assuming it's true, I probably haven't been consistent about it in the drawing.

<<FIRST <LAST WK INDEX NEXT WK> END>>

SEXI: I finally have a webcomic counterpart. Even if she’s going to jail.
QQUINN: I never stole anything. Only did what I felt was right. So Para freed me... sentenced to stay this way.
QQUINN: The worst part? Well never see Versine's good ideas. A wall around scientific notation, no more calculators...
SEXI: Good ideas for whom? Should progress be denied? Change is inevitable. We must adapt.
QQUINN: Fine, fine...
QQUINN: So how do you manage a proper workout with this extra curviness?
SEXI: You’ll adapt to that too. (pats QQuinn's shoulder)

Monday, 1 May 2017

S9.301 - Discouraging Words



Welcome to Series 9. New index page exists. I'm now drawing with new "B" (not HB) pencils I got for my birthday.
If you're simply clicking "next" you missed the Character Bible and Settings Info posts. I found that handy, reminding me of characters we hadn't seen for a while.

<<FIRST <LAST WK INDEX NEXT WK> END>>

QSIN: RhysPlus is off adjusting, so I’m out a vice president. Would your ArcSin be interested in the role?
NISANO: QQuinn had my missing science stuff! This is an outrage! We'll throw the book at her. Find a big book of science!
SOC: Equal Temperament.
NISANO: I feel like playing music. Oh, hello QSine, lovely day, yes? Fare thee well.
QSIN: As I was saying, would YOU be interested in the role, ArcCos?
SOC: Sure, thanks.

Thursday, 27 April 2017

Series 9: eVolution

SERIES 9: e-Volution INDEX


<- Back to Index 8

9.5 : Be Trade
9.6 : Side Kicks
9.7 : Tourism de Force
9.8 : Scan Dull
9.10 : 
9.11 : 
9.12 : 
9.13 : 
9:14 : 
9.15 : 
9:16 : 

Monday, 24 April 2017

Math Settings Info

Accurate up to and including Episode 300, so SPOILERS, obviously. Though this is not as plot revealing as it was last week, for characters.

In fact, locations were never really much of a consideration for me... Series 1 took place in Maud’s bar. Series 2 took place in Maud’s bar and at the Conic residence. Series 3 took place heading to the “Angle Zone”, which I loosely based on “Land of Oz”. Then Series 4 kicked everyone out into some new purgatory.

It was only starting with Series 5 that I started to give some thought to where some places might be in relation to other places. By the time of Episode 190, in Series 6, I had made a map. After all, that’s when Lyn said she was “writing out a map of our Purgatory” and that the characters were “living in a relatively similar configuration to how we were back in math”. Find a nicer version of that map below, along with some other key location data.


MATH SUBJECT MAP


Note the fact that there are roads is a bit misleading, since the characters don’t drive. The closest we’ve had is Expona’s motorcycle (and sidecar). Everywhere is reachable by walking, though it would likely take a day to get from one side of the map to the other. (No exact scale is available.) Most scenes occur in the vicinity of Maud’s bar, identified with |ABS|. Presumably, there are some other buildings in the vicinity (like Hyper’s research facility, or Sine’s Council room) which aren’t specifically labelled.



NOTES:
1. Polynomials. Episode 159 establishes that Para lives in an apartment. (It seems like it might be one room?) In fact, all known polynomials (so up to degree 6) live in that building, located at the base of Polynomial Way. Their polynomial children (x+1, 2x+1,5x-2, etc), referenced in Episode 101 and seen in Episode 259, live on the avenues which split off from Polynomial Way. All streets march off towards infinity, implying that you can never really enumerate all children.

2. Conics. They all live in the same mansion, which lacks right angles and consists of different conic sections. (Lyn found a path to Hyper’s lab using some Transverse Axes in Episode 39.) Part of the exterior is seen in Episode 237, though that was before unification, so it may appear a little different now. The Conics had also rigged an exterior alarm system, seen in Episode 44, and I suspect they’re positioned on a hill, though that’s not canon. Reci lives just down the road, being a hyperbola.

3. Trigonometry. Having their own zone, they don’t interact as much with the others, the Conics being the closest. (Tangent was said to have an external rental property as “Slope” in Episode 60, and Expona visited the “Bowditch” in Episode 244 before going in, so there must be some structures by the Off Road.) The place is a mashup of “Wizard of Oz” and “Star Trek” in terms of the locations and colour scheme. In the middle is “origin central”, where the older archaic trig (greens) hang out. No specific home location can be given for the trig in charge - as Circe said in Episode 62, “They’re constantly on the move”. Either all regional houses in the AZ are similar, or trig don’t have much material wealth to carry with them (or both).

4. Other Functions. Like 'Polynomial Way', the 'Root Route' heads to infinity, implying an uncountable set. Root lives near the base, then Radik... and presumably there’s structures to allow for a 4th root, et cetera, despite them not being formal characters. Opposite the downtown core to Polynomial Way, Exponent Place is a dead end. Expona only needs one house, as she can become all manner of different bases and transformations; if there are “children”, as with polynomials, they have never been referenced. (On the other hand, Para can transform too.) Meanwhile, although Logan spends much of his time in his gazebo Base (see below), presumably he has a house near Expona where he can kick back and relax too.

5. Subject Fog. This northern area is where the explorations of other subject areas took place in Series 4, with random, nebulous encounters of other personifications. The Beta Group likely never strayed far from the Off Road. Circe and Elly ran off this way towards the end of Series 6 and disappeared.

6. Stats Cliff. Called that because if you fall off, you’re “just a statistic” - unless you can fly out, as Para did in Episode 175. The “hidden bridge” was discovered by Reci in Episode 199, and it leads to the Jump Gate and Dial Out Device. Episode 218 provides the best look at that small plateau, along with the Gate, and a Hyper Jumper.


LOGAN’S BASE


Since it’s effectively a ship, it’s worth it’s own section. The exterior was first seen in Episode 106, resembling a gazebo, referred to by Logan as the “crow’s nest”. It is possible to have the subscript hatch open while the base is in flight. There is a phaser ring around the blue light at the top.

The best shot of the bridge occurred in Episode 150. The ladder at the back comes down from the hatch above, implying a lack of wheelchair accessibility, though gravity can be modified on the bridge, as a work-around. There are three consoles at the back, for Engineering, Security/Weapons, and Science. Opposite to them is the main view screen. In between is Logan’s purple easy chair, and another hexagonal console for navigation and operations. (An early version had a side exit towards engineering; this was scrapped.)


From Episode 150

The ladder at the back continues down into what must be some sort of complex hallway system. As ParaB said in Episode 110, “a single new room increases the complexity by a factor of ten”, and it takes some time for characters to get from one place to another, implying the rooms aren’t stacked on top of each other.

Such rooms would include: (1) a medical bay, where QT had conversations with some characters; (2) an engineering room with sliding doors, where Radik and Csc argued; and (3) living quarters, where the Step Functions were confined. Presumably the quarters are more functional than comfortable, as the characters preferred to stay in the Hilbert Hotel after arriving in Fractal City.

There may be other rooms within the ship, but (unless I missed something, which is possible) they have not been referenced. For instance, I’m pretty sure there isn’t a swimming pool like in the TARDIS, but you never know.


JUMP GATE NETWORK


Elizabeth Weierstrass explained about the network in Episode 192. There are at least eight jump gates. Travel between them is not instantaneous, meaning one could be lost in hyperspace (think “Babylon 5”), but it’s faster than any alternatives. They can be powered down, thus may work intermittently, but take about 1.21 gigawatts to activate. (After activation, they pull in minimal power.)
From Episode 204

The gates connect the following locations:

1. Fractal City. Their Jump Gate is located beneath the X-Mansion. Down there with it, is a control room, an interrogation room, a place to store Hyper Jumpers... it’s basically some crazy cross between StarGate Command and Xavier’s School for Gifted Youngsters. Other notable locations in the City include the Overline Bar, the Hilbert Hotel... and not much else is known.

2. Lesser Used Functions. This is where characters like Mae, Mink, Con... and even Gamma (not canon, but pretty sure) are from. It has never been seen. Also not seen, but strongly implied (by Julia in Episode 172) is that Fractal City is connected to this place via a “Heighway”. Meaning the portal is simply a faster route. (Do fractals drive? I’m not sure.)

3. The Steppe. This is where Signum, Hevvi, and Flora have a house. There may also be discrete functions living in this area, but that’s only a vague idea, far from canon. It may be possible to get from the Steppe to the other locations without portals, but there is no formal road. That would explain how Logan’s base crashed in the midst of nowhere, after leaving the Steppe.

4. Statistics & Probability. This gate is password protected. The fractals were not authorized to provide it - in fact, in the canon side story, the password was changed, barring them from accessing this location as well. Implying no way to otherwise access the land of Statistics. It’s not clear what this place looks like.

5. The Argand Plane (the Complex Plane). A place for plotting with the x-axis as reals and the y-axis as imaginaries. Nothing further is known.

6. Unknown 1. Acts as a beacon. Password protected. Non-canonically, I’ve wondered if there’s a Polar Plot out there somewhere. It may not have functions living there, but turns visiting functions weird. If so, the fractals have some knowledge of what it would do, based on the image shown to QT in Episode 196.

7. Unknown 2. Acts as a beacon. Password protected. Non-canonically, CF had to come from somewhere other than the Lesser Used Functions. Maybe this gate has something to do with sets? But then, maybe that’s part of probability instead. Who knows?

8. Math Subject. On the plateau off the edge of the cliff, it was added to the network by the main characters. But as Can-Tor determined in Episode 204, it lacked a regulator, and would have imploded, causing trouble to the existing network. It was taken offline, by being deliberately damaged. Although Can-Tor said it looks “beyond repair”, she also said the flux capacitor was scrap, yet it was retooled to send Logan’s Gazebo back in time.

Con was also seen using a portable portal device (as was Sine in the canon side story). Presumably these devices don’t let a person pop in just anywhere, in fact, my suspicion is that a person might have had to visit the location in some other way, to punch in the proper co-ordinates. But that’s non-canon, so as with anything else that hasn’t formally appeared, the logistics could be modified to suit a future plot as needed.


CONCLUSION


This post, and the previous one, have summarized all characters and locations. The plan is to launch Series 9 (e-Volution) next week! It will feature the return of an old character, along with a reference to the Analemma - both things you would already have been tipped off about by looking at the 2017 banner for the Facebook page. Just saying.

Thanks for reading. Hope you’ll return (or join us) for Episode 301.

Monday, 17 April 2017

Math Character Bible

Accurate up to and including Episode 300 (end of Series 8), so SPOILERS, obviously. Serial characters (entries 1-222) are listed first, followed by their WebComic counterparts wherever they exist (entries 223 on). Unification occurred at Episode 254, not quite doubling the cast. But don’t let me stop you if you have your own personified math characters in mind out there too... inspiring other versions is kind of the point, frankly.

Incidentally, this info took over 12 hours to compile and cross-check, not even including the drawing. Each drawing took at least a half hour to sketch, scan/position and colour (inking and erasing pencil lines felt a bridge too far, but including colours helps me for having them all in one place). That’s why some images are still to come (may come by the end of the week).

Has it really been almost six years? I must be out of my mind. With thanks to my wife, as I was a bit of a hermit for a couple days over Easter. Also to my 10 (?) regular readers. And you, thank you for dropping by! You can now vote for the serial part of this story on “Top Web Fiction”. (I'm working on the WebComic equivalent.)

Jump To:

*POLYNOMIALS*


1.
EQUATION: y = x

NAME: Lyn (Linear)
FIRST SEEN: Episode 1
APPEARANCE: Hair is polynomial blonde, eyes are odd function green. Wears blue overalls and glasses. Y-Intercept bow in hair. Body lacks curves (below drinking age). Her leading coefficient watch can call Tangent.
KEY HISTORY: First customer in Maud’s bar. Infiltrated Conics in standard form, to retrieve Para, under guise of “Directrix”. Went into “Angle Zone” with Circe to help Tangent, mind merging with Sine. Part of Group Beta, investigating alternate subjects. Mapped out their Purgatory region.

Math Traits:
ASSOCIATES: Polynomials
DEFAULT FORM: Slope-Intercept
INVERSE: (self inverse)
RECIPROCAL: Reci
Alternate Form: Standard Form. Loses the overalls, gains a skirt, and hair tints a non-function blue. Infinite eccentricity. (First seen Episode 31.)

COMIC NAME: QLyn
FIRST SEEN: Episode 223
DIFFERENCES: Hair is longer and braided diagonally on each side of her head. No glasses.
KEY HISTORY: Initially advocated war on decimals. First to notice the Serial-Comic tear. Has questioned her sexuality. Ran in the Math Election, later dropping out. Became minister of defence in QSine’s new cabinet.


2.
EQUATION: y = x^2

NAME: Para (Parabola, Quadratic)
FIRST SEEN: Episode 8
APPEARANCE: Hair is polynomial blonde, eyes are even function blue. Has bunny ears hairband, default up (minimized depression). Pink dress. Teardrop earrings. Y-Intercept bow around neck.
KEY HISTORY: Singer of Song Parodies. Beloved by Root, also QT. Kidnapped by Conics, resulting in creation of ParaB, with whom she’s shared a telepathic link. Got Expona to bring Tangent into the “Angle Zone” to help Lyn. Hung out with Group Gamma, talking current events, unable to record singing. Sank into depression in part over perception that humans hate quadratics. Had a near death experience falling off a cliff, resulting in an ability to sense beyond the fourth wall. She also leaned how to whirl her bunny ears like helicopter rotors, achieving flight. Had to break the news about Sine to Cosine, owing to her link with ParaB. Para later started up an orchestra, to help distract Trig. She did the Student’s tea distribution that QT and Sigma needed, for unifying with the Comic. Ran in the Math Election, lost to QSine. Encountered a parallel version (in #273). Became minister of justice (bunny ears lawyer) in QSine’s new cabinet.

Math Traits:
ASSOCIATES: Polynomials
DEFAULT FORM: Standard
INVERSE: Root
RECIPROCAL: Rhys
Alternate Forms: Vertex Form, gains a tiara and larger earrings. (First seen Episode 14.) Factored Form, dress gets a separate skirt, jacket appears, gains access to factor wand. (First seen Episode 19.)

COMIC NAME: QPara
FIRST SEEN: Episode 223
DIFFERENCES: Pink dress has collar and sleeves. Wears socks. No hairband, hair in twintails, default down (maximized depression). Y-Intercept bow in hair.
KEY HISTORY: Improper expansion is an anger trigger. Investigated whether there was support for QLyn’s war on decimals. Supported rallying behind QSine for president.


3.
EQUATION: y = x^3

NAME: Cubi (Cubic)
FIRST SEEN: Episode 25
APPEARANCE: Hair is polynomial blonde, eyes are odd function green. Has an inflected ponytail. Wears a blue robe, carries a bokken. Y-Intercept bow tied around waist.
KEY HISTORY: Once spoke with an inflection, starting all sentences with “Hey”. Her volume control and spline sense were handy in escaping a Conic trap.

Math Traits:
ASSOCIATES: Polynomials
DEFAULT FORM: Standard
INVERSE: Radik III
Alternate Forms: Factored Form, never seen, incorporates her bokken (always there, as always an x-intercept).

COMIC NAME: QCubi
FIRST SEEN: Episode 230
DIFFERENCES: Hair twintails model graph, Y-Intercept bow in hair.
KEY HISTORY: Seemed unconcerned about decimals.


4.
EQUATION: y = x^4

NAME: QT (Quartic)
FIRST SEEN: Episode 23
APPEARANCE: Hair is polynomial blonde, eyes are even function blue. Has cat ears hairband. Pink dress with puffed sleeves and pink boots. Y-Intercept bow on chest.
KEY HISTORY: Her biquadratic parts cause her to crush on Para. Called the meeting to rescue Para from the Conics. Part of Group Alpha, sent to explore. Acted as Medical Officer (IV training), created Quadcorder. Started romance with ParaB. Was then affected by Hevvi, making ParaB angry. First to meet Koch, when her ParaB relationship made her sleep in and be late for a meeting in Fractal City. She selected Sigma from CF’s novelties shop, and later interfaced with the cube. QT/Sigma’s power restored Math, and united the serial and webcomic. She then worked to try and make ParaB corporeal again. Was the first victim of the derivative virus. Donated an exponent of 2 to save Tangent, and was subsequently restored.

Math Traits:
ASSOCIATES: Polynomials
DEFAULT FORM: Standard
Alternate Form: Factored Form, gains a jacket and factor fork. (Seen as part of unison with Sigma, Episode 216.)

COMIC NAME: QQT
FIRST SEEN: Episode 232
DIFFERENCES: Hair twintails model graph, Y-Intercept bow in hair.
KEY HISTORY: Ignored by QPara, she helped Maud with his project. Leading to her wearing a silly outfit and being the one to make first contact with the Serial personifications.


5.
EQUATION: y = x^5

NAME: Quinn (Quintic)
FIRST SEEN: Episode 50
APPEARANCE: Hair is polynomial blonde, eyes are odd function green. Dangling strand of hair helps model graph. Japanese-style schoolgirl uniform in blue, skirt unevenly cut, V on socks. Y-Intercept bow tied on arm.
KEY HISTORY: Fired rocket launcher at Conics residence to save her friends.

Math Traits:
ASSOCIATES: Polynomials
DEFAULT FORM: Standard
Alternate Note: Quintic is the first polynomial with no solving formula, and she has no way to express certain exact factors. This makes her irrational, and has in part led to a vendetta against calculators.

COMIC NAME: QQuinn
FIRST SEEN: Episode 231
DIFFERENCES: Hair twintails model graph, Y-Intercept bow in hair.
KEY HISTORY: Suggested bombing calculators, later considered a diplomatic solution with Gamma. Joined Versine’s campaign and released the derivative virus. Then developed the integral cure, ending up as a sextic.


6.
EQUATION: y = x^6

NAME: Sexi (Sextic)
FIRST SEEN: Episode 52
APPEARANCE: Hair is polynomial blonde, eyes are even function blue. Has hairband with rounded ears. Pink dress with slit up the slide. Y-Intercept bow on dress/leg.
KEY HISTORY: Has demonstrated familiarity with higher dimensions and sexy primes. Makes rare appearances.
ASSOCIATES: Polynomials

Character has no Comic counterpart, though QQuinn now has her form.


*CONICS*


7.
EQUATION: x = y^2

NAME: ParaB (Parabola)
FIRST SEEN: Episode 51
APPEARANCE: Hair is non-function orange, eyes are conic blue/grey. Has bunny ears hairband like Para but with ears tilted to her left and a permanent tiara. Green dress. Moon shaped earrings and crescent necklace.
KEY HISTORY: Created when Hyper’s ZPM (Z-Axis Points Module) exploded by a mirror near Para, scrambling the parabola’s parametric equations. Had a telepathic link with the polynomial. Sees Root as a half brother, not a romantic interest. Singer of Song Parodies, statistical branch (eventually). Part of Group Alpha, sent to explore. Acted as Science Officer. Started romance with QT. Immune to Hevvi’s “turn on” influence, learned to attack by throwing her tiara (Focus Tiara Action). Was told by Koch “If you go to Stat’st’cs, you won’t die”. Was detained in Fractal City by Bert, but escaped thanks to Hevvi. Her idea is what united the serial and webcomic. Nearly merged back with Para, saved by Hyper, becoming incorporeal instead. Used her phased state to locate where QQuinn released the derivative virus.

Math Traits:
ASSOCIATES: Conics
ECCENTRICITY: One

Character has no Comic counterpart.



8.
EQUATION: x^2 + y^2 = r^2

NAME: Circe (Circle)
FIRST SEEN: Episode 34
APPEARANCE: Hair is non-function blue, eyes are conic blue/grey. Has five hair curlers (representing five points to define a conic, Ax^2+Bxy+Cy^2+Dx+Ey=F). Purple dress. Large round earrings and necklace with five round beads.
KEY HISTORY: The mastermind behind the plan to kidnap Para. She grudgingly accompanied Lyn into “Angle Zone”, delivering a series of Specials to explain Trigonometry in the context of the Unit Circle. Helped evacuate before Versine’s explosion. Hung out with Group Gamma, talking current events. Escaped with Elly before the Jump Gate blew, has not been seen since.

Math Traits:
ASSOCIATES: Conics
ECCENTRICITY: None

Character has no Comic counterpart.



9.
EQUATION: (x/a)^2 + (y/b)^2 = 1

NAME: Elly (Ellipse)
FIRST SEEN: Episode 37
APPEARANCE: Hair is non-function purple, eyes are conic blue/grey. Has a hairband with two elliptical orbits surrounding her head. Light blue off the shoulder top, dark blue yoga pants, belt of ovals. Hoop earrings and necklace with elliptical stone.
KEY HISTORY: Likes Ovaltine, and her meditative style was a calming force for the conics. Became part of Group Beta, investigating alternate subjects. Acted as psychiatrist to Para when she was depressed. Sensed the Q-Comic versions early, with a ritual in the “Angle Zone”. Escaped with Circe before the Jump Gate blew, has not been seen since.

Math Traits:
ASSOCIATES: Conics
ECCENTRICITY: Mild (0 < e < 1)

COMIC NAME: QElly
FIRST SEEN: Episode 237
DIFFERENCES: Hair is done up in a pair of ellipses, held in place with ‘+’ hairbands. Wears a blue asian-style dress with a slit up the side. Uses a protractor/chakram as a weapon.
KEY HISTORY: Prevented QHyper from giving QPara drugged tea. Sensed the Serial versions early (like her counterpart). Was affected by the derivative virus.



10.
EQUATION: (x/a)^2 - (y/b)^2 = 1

NAME: Hyper (Hyperbola)
FIRST SEEN: Episode 34
APPEARANCE: Hair is non-function green, eyes are conic blue/grey. Hair curves out in four directions. Orange top, green skirt, purple shoes, often a lab coat. Two asymptote rings, double crescent earrings and a necklace with an hourglass shape.
KEY HISTORY: Began as a mad scientist with a focus on two things, accidentally creating ParaB with her ZPM. Created a railgun to fire axes which re-bent Maud’s hair. Created the Cone of Science to communicate with Group Alpha, but needed help from Nisano, and only got it to work by invoking magic. Switched to being a “madgical” girl. Believed Sigma was her magical guide, and interfaced via QT to restore ParaB (incorporeally). Helped bring Maud back in time on Logan’s base. Briefly went along with Versine’s campaign (possibly to spite QHyper). Finally interfaced with Sigma alone in a (failed) attempt to restore ParaB’s solid form.

Math Traits:
ASSOCIATES: Conics
ECCENTRICITY: Severe (1 < e < infinity)

COMIC NAME: QHyper
FIRST SEEN: Episode 237
DIFFERENCES: Hair still curves four ways, but is held in place with a ‘-’ hairband. Her top has a collar, her skirt has pleats, and she wears tall green boots.
KEY HISTORY: Tried to get QPara to join conics using drugged tea. Considered the Serial personifications “imaginary”, backing QSine for president. Became minister of innovation/science in QSine’s new cabinet.



*TRIGONOMETRY*


11.
EQUATION: y = sin(x)

NAME: Sine (Sine)
FIRST SEEN: Episode 58
APPEARANCE: Wavy brown trig hair, bangs/fringe showing graph. Brown eyes. Red T-Shirt showing O over H. DRG Belt and jeans.
KEY HISTORY: Along with her twin sister, Cosine, she caused their younger sister Tangent to leave the “Angle Zone”. Mind merged with Lyn in order to create sin(x)/x, who could prevent Versine from blowing them up with the TI n-Spire. Part of Group Alpha, sent to explore. Acted as Logan’s executive officer (though couldn’t settle on one role). Used sign language to communicate with Signum. Met Mink and Con. Teleported with the Cone of Science during Hevvi’s attempt to take over the ship. Sacrificed herself to save Logan’s ship from the Hilbert Curve. Presumed dead, as only her period cane remained.
CANON SIDE STORY: Trapped between dimensions, Sine befriended a human girl named Rosemary Thorne, who helped her to return to Fractal City (long after the others had left).

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: ArcSin
RECIPROCAL: Cosecant

COMIC NAME: QSine
FIRST SEEN: Episode 245
DIFFERENCES: Pants are a slightly darker shade, as is her skin. Has Cosine as an alternate form, not a twin, but that’s not common knowledge.
KEY HISTORY: Acted as a diversion while other Qtrig worked on building a ship. Got along well with Serial-tans (perhaps as they had no Sine). Ran in the Math Election, was elected President via a twitter poll (of non-readers). Made ArcSin vice president and assembled a cabinet. Co-ordinated investigation into derivative virus.



12.
EQUATION: y = cos(x)

NAME: Cosine (Cosine)
FIRST SEEN: Episode 58
APPEARANCE: Wavy brown trig hair, bangs/fringe showing graph. Brown eyes. Red T-Shirt showing A over H. DRG Belt and jeans.
KEY HISTORY: Along with her twin sister, Sine, she caused their younger sister Tangent to leave the “Angle Zone”. Saw to the evacuation of everybody before the TI n-Spire explosion. Part of Group Beta, investigating alternate subjects. Sensed Sine being absorbed by the Hilbert Curve, cried uncontrollably, fell into depression. Played violin in Para’s orchestra, which helped. Had to morph to the form of ‘1-cos(x)’ to allow Maud and Signum to locate Versine. Was happy to meet QSin.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: ArcCos
RECIPROCAL: Secant

Character’s Comic counterpart was QSine, since in degrees, cos(x) = sin(x+90)



13.
EQUATION: y = tan(x)

NAME: Tangent aka Slope (Tangent)
FIRST SEEN: Episode 6 (as Slope); Episode 58 revealed her trig nature.
SLOPE APPEARANCE: Brown trig hair, face framing bangs showing graph. Brown eyes. Green ball cap showing ‘m’. Yellow midriff baring shirt showing ‘X’, but is ‘Y’/‘X’ when including collar (possibly with pink undershirt). DRG Belt and jeans. Asymptote ring.
TAN APPEARANCE: Brown trig hair, face framing bangs showing graph. Brown eyes. Red T-Shirt showing O over A. DRG Belt and jeans. Asymptote ring. Shortest main trig.
KEY HISTORY: As Slope, communicated with Lyn, and joined the polynomial raid to retrieve Para. Decided to leave the “Angle Zone” due to teasing by her sisters, but returned (with Expona) when she learned Versine was trying to blow everyone up. Tangent held off the TI n-Spire explosion with her asymptote ring until Sine could save them. She coordinated (via Lyn) between Gamma and Beta groups. Sought help for Cosine after Sine’s death, and stuck with her sister during the Comic unification. Was affected by the derivative virus, lost her square to QArcSin, then regained it from QT.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: ArcTan
RECIPROCAL: Cotangent

COMIC NAME: QTangent
FIRST SEEN: Episode 246
DIFFERENCES: Pants are a slightly darker shade, as is her skin. Her entire hair curves like her graph, not merely her bangs.
KEY HISTORY: Interjects whenever there’s something on her mind.



14.
EQUATION: y = csc(x)

NAME: Csc - female (Cosecant)
FIRST SEEN: Episode 87
APPEARANCE: Brown trig hair, half up and half down like her graph. Brown eyes. Yellow button up shirt with a red reciprocal tie showing H over O (with an XMas tree). DRG Belt and jeans.
KEY HISTORY: Sworn defender of Sine. Part of Group Alpha, sent to explore. Acted as Security officer. Was bewitched by Hevvi. Argued with Radik about security measures. Met Mink and Con. Enacted a protocol making gravity undefined on the ship’s bridge to prevent a takeover. Her phaser fire got them out of the Hilbert Curve. She was shattered by Sine’s apparent death. Joined Logan in the Overline bar, seeing Statistics through perception filters. Was present for QT’s first union with Sigma, on the ship.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: ArcCsc
RECIPROCAL: Sine

COMIC NAME: QCoSec
FIRST SEEN: Episode 249
DIFFERENCES: Jeans replaced with a skirt, very dark skin. Likely has QSecant as an alternate form.
KEY HISTORY: Cleared Qtrig out of a building after a Versine gas attack.


15.
EQUATION: y = sec(x)

NAME: Sec (Secant)
FIRST SEEN: Episode 87
APPEARANCE: Brown trig hair, raised on each side and down in the middle like her graph. Brown eyes. Yellow button up shirt with a red reciprocal tie showing H over A (with a smile face). DRG Belt and jeans.
KEY HISTORY: Sworn defender of Cosine. Part of Group Beta, investigating alternate subjects. Threatened Hyper and Nisano when Cosine feared that Sine had died. Played viola in Para’s orchestra. After unification, became concerned when the derivative virus made Tangent’s hair into a version of hers.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: ArcSec
RECIPROCAL: Cosine

Character seems to have no Comic counterpart. Likely exists as alternate form of QCoSec.



16.
EQUATION: y = cot(x)

NAME: Cot (Cotangent)
FIRST SEEN: Episode 86
APPEARANCE: Short brown trig hair, face framing bangs rising up to show graph. Brown eyes. Yellow button up shirt with a red reciprocal tie showing A over O. DRG Belt and jeans. Asymptote ring. Tallest reciprocal trig.
KEY HISTORY: Considered their “chief engineer”, occasionally slips into a Scottish accent. Used her asymptote ring to support Tangent in the TI n-Spire incident. Helped Root connect the blog. Fixed the replimator in Maud’s bar. Helped hook the flux capacitor into the Jump Gate.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: ArcCot
RECIPROCAL: Tangent

COMIC NAME: QCoTan
FIRST SEEN: Episode 248
DIFFERENCES: Jeans replaced with a skirt, very dark skin.
KEY HISTORY: Seems prone to spacing out and making odd suggestions.



17.
EQUATION: y = arcsin(x)

NAME: Nis aka “Dr Nisano” (Arcsin)
FIRST SEEN: Episode 104 (in room during Ep 86)
APPEARANCE: Brown trig hair in a mohawk to show graph. Brown eyes. Blue shirt with a theta showing +/- quadrants. DRG Belt and jeans. Also tends to wear yellow glasses with green swirls and the occasional lab coat.
KEY HISTORY: Nisano created his goggles “with Science”. Identified a problem with Hyper’s Cone of Science and started competing with her. Became even more manic after the loss of Sine, his twin brother Soc becoming concerned. Joining Para’s orchestra (playing double bass) helped calm Nis down. He worked with Soc on the Dial Out Device. “Dr. Nisano” was then brought back, due to the time deadline for preventing the Jump Gate explosion. Nisano helped bring Maud back in time on Logan’s base.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: Sine

COMIC NAME: QArcSin
FIRST SEEN: Episode 247
DIFFERENCES: Darker skin. No swirly glasses, may wear shades.
KEY HISTORY: Briefly affected by imaginary gas while doing Science. Created “Decimal Buster” device. Appointed Vice President by QSine. Affected by derivative virus, which combined with a square to turn him into RHYSPLUS. Character NO LONGER EXISTS in this form, see RHYSPLUS.



18.
EQUATION: y = arccos(x)

NAME: Soc (Arccos)
FIRST SEEN: Episode 136 (in room during Ep 86)
APPEARANCE: Brown trig hair in a mohawk to show graph. Brown eyes. Blue shirt with a theta showing +/- quadrants. DRG Belt and jeans.
KEY HISTORY: Works science with his twin brother “Nisano”. Fearing for ArcSin’s sanity, advised Nis to stop wearing the swirly glasses. Allowed it again when under time pressure to prevent the Jump Gate explosion.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: Cosine

Character seems to have no Comic counterpart. Likely existed as alternate form of QArcSin.



19.
EQUATION: y = arctan(x)

NAME: Nat (Arctan)
FIRST SEEN: Episode 83
APPEARANCE: Brown trig hair swishing to his right to show graph. Brown eyes. Blue shirt with a theta showing +/- quadrants. DRG Belt and jeans. Shortest trig inverse.
KEY HISTORY: Skilled medic. Was the first to be told about Versine’s TI n-Spire bomb. Part of Group Beta, investigating alternate subjects. He looks out for Nis and Soc, was troubled by Hyper’s association with them. Nat helped Elly talk with Para when the latter was depressed. He received a write-in vote during the election, leading to him becoming minister of health in QSine’s new cabinet. Did an analysis of the derivative virus and its cure.

Math Traits:
ASSOCIATES: Trigonometry
INVERSE: Tangent

COMIC NAME: QArcSin
FIRST SEEN: Episode 248
DIFFERENCES: Darker skin.
KEY HISTORY: Helped with trig ship building. Was pleased by the write-in election vote.



20.
EQUATION: y = vers(x) = 1-cos(x)

NAME: Versine (Versine)
FIRST SEEN: Episode 69 (posing as OneMinusCos); Episode 93 (in green)
APPEARANCE: Wavy brown trig hair, bangs/fringe showing graph (essentially a reflected cosine lifted a bit higher). Brown eyes. Green T-Shirt, unlabelled. Belt and jeans.
KEY HISTORY: Misses the old days, when she was more popular. Attempted to blow up main trigonometry with a TI (Tangent Issue) n-Spire, in order to seize control of the “Angle Zone” during the confusion; it was not her first attempt take over. After Series 3 she became a point of reference (and cause of arguments) among the other personifications to find math, as she wasn’t with them for Series’ 4 through 6. Versine ran in the Math Election, campaigning to fight calculators, separate math from the curriculum, and crush all “new math”. When she lost, Versine refused to recognize QSine as president, until she was made minister of public services in QSine’s new cabinet. She devised a plan to take over the election system and steal votes (as her derivative is Sine). Although she did scrap it, the derivative virus was unleashed (incorrectly) by her supporter, QQuinn.

Character is her own Comic counterpart.


21.
EQUATION: y = exsec(x) = sec(x)-1

NAME: Exsecant (Exsecant)
FIRST SEEN: Episode 76 (posing as a Secant); Episode 94 (revealed)
APPEARANCE: Brown trig hair, raised on each side and down in the middle, though shorter in length than Secant. Brown eyes. Green shirt, unlabelled. Belt and jeans.
KEY HISTORY: Working with Versine, attempted to prevent anyone from entering the building containing the TI bomb. Was forced to pay a fine for impersonating a security officer. Recently seen in the audience of one of Versine’s election rallies.

Character is her own Comic counterpart.



22.
EQUATION: y = arccot(x)

NAME: Toc (Arccot)
FIRST SEEN: Episode 93
APPEARANCE: Bald, with a unibrow modelling his graph. Brown eyes. Purple button up shirt with a blue reciprocal tie showing a theta. DRG Belt and jeans. Tallest reciprocal trig inverse.
KEY HISTORY: Penchant for making lawyer-like “Objection!”s. Played cello in Para’s orchestra. Seems to have no Comic counterpart.

23a.
EQUATION: y = arccsc(x)
NAME: Csc - male (ArcCosecant)
FIRST SEEN: Episode 87
APPEARANCE: Bald, with both eyebrows modelling his graph. Brown eyes. Purple button up shirt with a blue reciprocal tie showing a theta. DRG Belt and jeans.
KEY HISTORY: Once spoke briefly. Was presumably in Para’s orchestra.

23b.
EQUATION: y = arcsec(x)
NAME: Ces (ArcSecant)
FIRST SEEN: Has not formally appeared, implied to be wherever ArcCsc is.
APPEARANCE: See ArcCsc.



*COMMON FUNCTIONS*


24.
EQUATION: y = b^x

NAME: Expona (Exponential)
FIRST SEEN: Episode 81
APPEARANCE: Redhead with freckles, her hair fringe arcing sharply up to her left in exponential growth. Hazel eyes. Wears leather button-up vest, leather pants and red boots. Coefficient watch on her right hand, as she is left handed. Asymptote ring, yellow stud earring, and occasionally a base tattoo.
KEY HISTORY: Engaged in a one-sided rivalry with Para, as she’s fed up with exponentials being mistaken for quadratics. Brought Tangent into the “Angle Zone” using her motorcycle, and led Exsecant away on a chase. Became singer of Song Parodies, musicals branch, to compete with Para. Hung out with Group Gamma, talking current events. Her constantly talking down to Para contributed to the parabola’s depression. While Expona felt uneasy once she realized that, she remained bitter about the parabola’s pivotal role in communicating with ParaB, and jealous over how everyone turned to the blonde for help (including for Para’s orchestra idea after Sine’s demise). Expona tried to spearhead a candidate discussion prior to the election, and when Para was chosen, declared that she would run against the parabola. But following a talk with QExpona, she dropped out. Expona became minister of finance in QSine’s new cabinet, and was finally given a chance to shine when QSine pointed out that e^x was immune to the derivative virus. Her investigation led to discovering the cause, pointing the finger at Versine.

Math INVERSE: Logan

COMIC NAME: QExpona
FIRST SEEN: Episode 233
DIFFERENCES: Paler skin tone, zippered vest, darker ankle boots, and wears eyeshadow.
KEY HISTORY: Claims to have occasional anger issues. Demonstrates a greater desire to help QPara (compare her counterpart), though is dismissive of the parabola too. Went looking for trigonometry, to ask about the decimal war. Also tried to spearhead a candidate discussion prior to the election, and she seemingly supported QSine. Tried to speak with Expona about her Para issues.



25.
EQUATION: y = log_b(x)

NAME: Logan (Logarithm)
FIRST SEEN: Episode 102 (was with Expona in Episode 99)
APPEARANCE: Redhead with freckles, his hair fringe arcing slowly off to his left in logarithmic growth. Hazel eyes. Wears a pirate style white shirt with a black vest and black pants. Has red boots, belt is a red sash. Coefficient watch on his right hand, as he is left handed. Asymptote ring, single hoop earring (right ear), and an eyepatch on his right eye, which covers his base.
KEY HISTORY: Leader of Group Alpha, sent to explore. Owns a ship that looks like a gazebo (his base is a subscript inside), which turned up one day as “a gift” from “The Professor”. Kept a Captain’s Log, assigning duties to everyone else. Showed he was slow to pick up on cues, as they encountered the Step Functions, and continued on to Fractal City. Became irritated as others constantly modified his base without doing proper testing. After Sine’s demise, effectively appointed Cosecant as his new right-hand-woman. Introduced everyone to the Fractal City Council. Accompanied QT to see the Characteristic Function. The fractal-like properties of his ship allowed CanTor to fly it through the Jump Gate network. Later, the flux capacitor was integrated into his ship, letting him bring Maud back in time. Finally, interested in expanding his domain (from x > 0), Logan took the derivative virus, becoming a new Reci. Character NO LONGER EXISTS in this form, see RECI.

Math INVERSE: Expona

COMIC NAME: QLogan
FIRST SEEN: Episode 251
DIFFERENCES: Paler skin tone.
KEY HISTORY: Has showed himself to be unaware of most of what was going on. Spent time at Versine’s rallies. Has now inherited Logan’s base.



26.
EQUATION: y = root(x)

NAME: Root (square root)
FIRST SEEN: Episode 16
APPEARANCE: Long silver-grey hair, with antenna strands hooking out to the left like his graph. Hazel eyes. Purple golf shirt, belted yellow pants and brown shoes. Usually carries a pad or other technological device.
KEY HISTORY: Initially diagnosed as bipolar, with positive or negative swings, now his mood seems to have settled into a general confusion. Able to get root access to most databases. By looking into tech ways for Para to open sideways, he prompted the conic kidnapping of Para. Tends to take his dislike of Conic antics out on Reci. Connected the blog, with help from Cotangent. Part of Group Beta, investigating alternate subjects, where he tended to propose things that already existed, only indirectly steering them to music. Cares about Para to the point of picking up on her depression and trying to help. Offered technical help to Nisano when the Jump Gate was going to blow. Encountered a parallel version (in #273). Was affected by the derivative virus (briefly giving him a tie).

Math Traits:
ASSOCIATES: Radicals/Surds
INVERSE: Para (for x > 0)
Alternate Form: When “on duty”, gains a headband showing horizontal/vertical transformation, his device showing any other (vertical) component. (First seen Episode 21.)

COMIC NAME: QRoot
FIRST SEEN: Episode 251
DIFFERENCES: Lower part of his hair also curves left.
KEY HISTORY: Seems to go along with whatever others around him are doing.



27.
EQUATION: x = y^3

NAME: Radik III (Cube Root)
FIRST SEEN: Episode 99
APPEARANCE: Short silver-grey hair, arcing to either side like his graph. Blue military suit, with tall boots. Has a purple sash and a badge showing the arrangement of cubic roots in polar coordinates. Caries a sword.
KEY HISTORY: His imaginary roots give him vague insights, leading to a superiority complex. Part of Group Alpha, sent to explore. Acted as Engineer, bickering with Cosecant because he wanted Security. Did install an Emergency Braking System. Sniped at the seeming romance between QT and ParaB, believing only arranged marriage between a function and their inverse was proper. Saw the Comic Q-tans as refugees, and has talked down to QElly.

Math Traits:
ASSOCIATES: Radicals/Surds
INVERSE: Cubi

COMIC NAME: QRadik
FIRST SEEN: Episode 251
DIFFERENCES: None of note.
KEY HISTORY: Disliked the election, likes QCubi.



28.
EQUATION: y = 1/x (xy = 1)

NAME: Reci (Reciprocal)
FIRST SEEN: Episode 26
APPEARANCE: Black hair, in two pieces curving opposite ways. Brown eyes. White shirt, grey suit jacket, blue pants, brown shoes. Blue reciprocal tie, two asymptote rings. Stubble.
KEY HISTORY: Never really on top of things, prefers extreme solutions. Helped Quinn aim to hit Hyper’s lab to save Lyn and Para (knowing the location owing to being a hyperbola himself). Ran video equipment for Group Gamma. Discovered the path off the cliff, leading to the Jump Gate. Tried to get people to call him Rhys (pronounce ‘Reese’). Ran in the Math Election, since it was all women, but then dropped out. Was affected by the derivative virus, and decided to keep the new gender form. For this Reci, SEE RHYS. Old LOGAN is now the NEW RECI.

Math Traits:
ASSOCIATES: Hyperbola (Conics)
INVERSE: (self inverse)
RECIPROCAL: Lyn

Character has no Comic counterpart. (Likely handled by Hyper.)



29a.
EQUATION: y = 1/x^2

NAME: Rhys (A Rational Function)
FIRST SEEN: Episode 289
APPEARANCE: Black hair, in two mirror images curving from out to up. Brown eyes. White shirt, blue pants, brown shoes. Reciprocal tie and asymptote rings.
KEY HISTORY: Formerly Reci, infected by the derivative virus. As he had been trying to use the name Rhys, he decided to use it for this female form. She managed to disengage the reflection that had resulted at first transformation.


29b.
EQUATION: y = 1/(a+x^2)

NAME: RhysPlus (A Rational Function)
FIRST SEEN: Episode 300
APPEARANCE: Grey hair in three parts when a < 0. Resembles Rhys when a = 0. All parts connect when a > 0. “a” value is connected to a pendant around his neck.
KEY HISTORY: Formerly QArcSin, infected by the derivative virus. While unstable, absorbed a square from the derived Tangent, creating equation 1/(1-x^2). Finally stabilized in RhysPlus form.



30.
EQUATION: y = |x|

NAME: Maud (Modulus/Absolute Value)
FIRST SEEN: Episode 1 (disguised)
APPEARANCE: Black hair with bangs lifting in a ‘V’; initially bent by being under a hat, then bent again due to Hyper, finally straightened. Blue eyes, initially hidden by sunglasses. Wears green sweater having darker green pointed band, white pants, blue shoes.
KEY HISTORY: Brought to High School Math by TPTB (Transcendental Pi-Type Beings), he opened an absolute value bar. Met the polynomials, let them use the place to plan the assault on the Conics. Got Circe to accompany Lyn into the “Angle Zone”. After over a year of observation, TPTB made him choose whether there was any purpose in continuing “personified math”. Maud’s decision to keep going was overruled, but he had created digital backups, which threw everyone out into a Purgatory (at Episode 100). When attempts to do videos and otherwise call attention to the ongoing serial (through work with Group Gamma) failed, Maud opened a new bar. He tried to help Para with her depression, and used the bar’s replimator to create instruments for Para’s orchestra. Was eventually reunited with his step-sister Signum for the attempt to point the way back to Versine and High School Math. After the serial and webcomic became united, he convinced Logan to bring him back in time, to the start of that webcomic, hoping to convince them that the serial format was superior. He recruited QQT, but only succeeded in convincing her that the very existence of a serial was inconsequential; Maud ended up making a snide remark to his past self before he went back. He then acted as a reporter during the Math Election, announcing the final results.

Character is his own Comic counterpart.



*STEP FUNCTIONS*


31.
EQUATION: y = sgn(x)

NAME: Signum (Signum/Sign)
FIRST SEEN: Episode 133
APPEARANCE: Hair’s right (-) side is pink, left (+) side is white/grey, with purple earrings to match signs. The colour coding extends to her track outfit, which also has a purple zipper down the middle and golden cuffs. Her (-) twintail is low (output -1) and her (+) twintail is high (output +1). Has grey eyes, pink eyeshadow.
KEY HISTORY: Hard of hearing, can communicate with sign language. Lived on a steppe with Hevvi and Flora. Her ability is to point precisely towards anyone she knows, except she’s rubbish at knowing their distance (needs Maud for that). Joined Logan’s ship to navigate, then reluctantly went along with Hevvi’s attempt to take over. Willingly went with ParaB to rejoin Maud, and they helped point the way back to High School Math. Has since been seen with him while he was reporting, carrying a camera.

Character is her own Comic counterpart.



32.
EQUATION: y = H(x)

NAME: Hevvi (Heaviside) - the ‘h’ is silent
FIRST SEEN: Episode 128
APPEARANCE: Hair’s right (-) side is black, left (+) side is white/grey, with yellow ‘u’ earrings (alternate notation). The colour coding extends to her track outfit, which has a yellow zipper down the middle and golden cuffs. Her (-) twintail is middling (output 0) and her (+) twintail is high (output +1). Has grey eyes, blue eyeshadow, glasses, and is on the heavy side.
KEY HISTORY: Hard of seeing, needs her glasses. Lived on a steppe with Signum and Flora. Her ability is to “turn on” other functions, making them do her bidding. The ability failed on ParaB (who is not a function), and Hevvi was subdued. She insisted on accompanying Signum into Logan’s base, and likely convinced Flora to investigate the circuits, forcing an emergency landing. She was subsequently knocked out by Con. After another attempt to completely take over the ship failed, Hevvi reluctantly worked with the others to investigate Fractal City. She ended up helping ParaB to escape, using a modified version of her ability; it sends out a blast of pleasure to non-functions, knocking them out. ParaB dropped Hevvi off at the steppe before bringing Signum to Maud.

Character is not accessible at time of Entry #300.



33.
EQUATION: y = floor(x)

NAME: Flora (Floor, or Ceiling)
FIRST SEEN: Episode 138
APPEARANCE: Hair’s right side is black and left side is white/grey, but she has three sets of hair curlers mimicking that same demarkation on each side of her head, with them rising from her right to her left. Her track outfit is black and white/grey stripes, with a whiter zipper running down the middle, and golden cuffs. Her white earrings are L-like, modelling the floor notation. Has grey eyes, golden eyeshadow.
KEY HISTORY: Doesn’t speak, though seems capable of it. Lived on a steppe with Signum and Hevvi. Her ability is a localized increase in gravity (“floor”) effect, which can also be reversed to send one to the ceiling (spinning her earrings upside down, entry 176). Takes her cues from Hevvi, likely including removal of a piece of Logan’s base that required an emergency landing, and definitely including the mutiny. In Fractal City, she stepped forwards to represent the steppe on Council, becoming the swing vote in bringing CF to town. She then used her pull to get a Hyper Jumper, in order to return home. But having had some part in ParaB’s escape, she may not be welcome back; she remains with Hevvi.

Character is not accessible at time of Entry #300.



*FRACTALS*

(all seeem somewhat super deformed, with smaller bodies)

34.
NAME: Dr. Elizabeth Weierstrass (Weierstrass function)
HAUSDORFF DIMENSION: 1.5
FIRST SEEN: Episode 191
APPEARANCE: Grey hair modelling a weierstrass graph (terrible split ends), green earrings denoting ‘0’ and ‘Tau’ (the period for trig). Green eyes. Wears a green uniform with red bands at the shoulders.
KEY HISTORY: The main diplomat for Fractal City and head of their Advisory Council. She explained to everyone about the Jump Gate network (#192), the illusion of race and other perception filters (#196), and introduced the full Council (#200). When the exploding Jump Gate problem became apparent, she tried to broker a mutually agreeable solution.



35.
NAME: Candice Torrent “CanTor” (Cantor Set/Dust)
HAUSDORFF DIMENSION: log_3(2)
ASSOCIATES: Base-Motif Fractals
FIRST SEEN: Episode 182 (background); Episode 193 (filters off)
APPEARANCE: Hair is a brown strip that constantly fragments up like Cantor Dust until it seems to vanish. Grey eyes and pink eyeshadow. Wears a pink tank top, a blue skirt and yellow shoes. Her skirt has black stripes mirroring the Cantor Set.
KEY HISTORY: The main inventor for Fractal City. She helped Weierstrass demonstrate perception filters, and was the one to discover the Jump Gate explosion problem. She helped Logan’s base navigate the Jump Gate system, rigged an explosive to destroy the gate, and was subsequently trapped, cut off from Fractal City. She assisted with the Polar Plot video set of 2014 and has been seen worrying about the High School functions.

Can-Tor is the only fractal character currently accessible within the Comic.



36.
NAME: Julia Childset (Julia Set)
HAUSDORFF DIMENSION: 2, for determined values of c
ASSOCIATES: Formula Iteration Fractals
FIRST SEEN: Episode 172
APPEARANCE: Brown hair has wavy curls, including a ponytail that spirals off into nothing. It’s held in place with spiral feathers, she has yellow spiral earrings, and her blue eyes spiral in tint. Wears a blue off-one-shoulder dress with a yellow Julia Set design on one side. This changes slightly when she is replaced in #198, as do her black shoes.
KEY HISTORY: Sits on the Advisory Council. She contacted Logan’s ship to warn about the Hilbert Curve, and set up their meeting with Statistics. Upon realizing their perception of Statistics was unclear, she got Weierstrass involved. Her later incarnation was seen on Council at the main table, and she brought Logan and QT to see CF. Hevvi knocked her out during ParaB’s escape.
CANON SIDE STORY: Julia cooked up some pills that could bring humans into their world, though she had no means of delivering them.


37.
NAME: Howie Mandelbrot (Mandelbrot Set)
HAUSDORFF DIMENSION: 2
ASSOCIATES: Formula Iteration Fractals
FIRST SEEN: Episode 182
APPEARANCE: Bald, but with a black soul patch on his chin shaped like the Mandelbrot set. His yellow eyes are also Mandelbrot shaped, and the image further appears on his tie. Wears a dark shirt and even darker pants.
KEY HISTORY: Sits on the Advisory Council. He’s a professor at the X-Mansion, a school for fractal education, constructed over the city’s Jump Gate. While skeptical of the High School relations’ potential after seeing their reaction to Statistics, he was not against bringing them to meet the Council. In attempting to stop ParaB during her escape, she knocked him out with her tiara.



38.
NAME: Koch (Koch Curve; three form the snowflake)
HAUSDORFF DIMENSION: log_3(4)
ASSOCIATES: Base-Motif Fractals
FIRST SEEN: Episode 183
APPEARANCE: Unknown. He resides in an encounter suit, with a headpiece shaped like a Reuleaux triangle; it contains a green Koch snowflake that can iris open and shut. His collar consists of two overlapped triangles and he wears a purple cloak beneath.
KEY HISTORY: Sits on the Advisory Council, often abstains from votes. Described as one of the earliest fractal curves. He first spoke cryptically to QT, foreshadowing her meeting with CF, then told ParaB “If you go to Stat’st’cs, you won’t die.” He later saw ParaB as she made her escape but did not stop her, merely confirming how “understanding is a three edged sword”.



39.
NAME: Henon Mappe (Henon Map)
HAUSDORFF DIMENSION: 1.26 (approx)
ASSOCIATES: Formula Iteration Fractals
FIRST SEEN: Episode 200
APPEARANCE: Black hair with blue highlights showing the Henon Map. Brown hair. Wears a red Chinese style robe decorated with white bows, has white earring studs.
KEY HISTORY: Sits on the Advisory Council, voted against the High School relations. Felt their formulas were too restrictive, and that they would attract attention of TPTB.



40.
NAME: Bert Hill (Hilbert Curve)
HAUSDORFF DIMENSION: 2
ASSOCIATES: Base-Motif Fractals
FIRST SEEN: Episode 200
APPEARANCE: Dark hair each side of his head, wears an item between modelling the start of a Hilbert Curve. Brown eyes. Dark red sweater, lighter red pants, gloves and a purple cape.
KEY HISTORY: The main security coordinator for Fractal City, voted against the High School relations. Believes “we fractals are the future, not them”. Badgered Can-Tor about the gate issue, insisted ParaB stay if Can-Tor was going, and confined the conic to an interrogation room. Hevvi knocked him out during ParaB’s escape.



41.
NAME: Vicsek “Vic” Fontaine (Vicsek Fractal/Cross)
HAUSDORFF DIMENSION: log_3(5)
ASSOCIATES: Base-Motif Fractals
FIRST SEEN: Episode 182
APPEARANCE: Grey patches of hair model the Vicsek Cross over his head. Light grey eyes. Sports a bow tie and a purple lounge suit.
KEY HISTORY: The main entertainer for Fractal City. He runs the Overline Bar, frequented by Statistics. Was also perceived by Radik III prior to being seen in the Council room.


.
42.
NAME: Sir Pinski (Sierpinski Triangle)
HAUSDORFF DIMENSION: log_2(3)
ASSOCIATES: Base-Motif Fractals
FIRST SEEN: Episode 200
APPEARANCE: Dark Sierpinski triangles on either side of his head. Grey eyes. Wears a monocle and kufi cap. His green robe has a yellow V at the top.
KEY HISTORY: The main architect for Fractal City, voted against the High School relations. He never explained his reasoning.


.
43.
NAME: Mel Blancmange (Takagi/Blancmange Curve)
HAUSDORFF DIMENSION: 1
FIRST SEEN: Episode 200
APPEARANCE: Wears an orange turban stacked like the Blancmange graph. Has a small moustache. Has a long white top, possibly a kurta.
KEY HISTORY: The main psychologist for Fractal City. Seemed inclined to abstain from votes.

.

*LESS COMMON FUNCTIONS*


44.
EQUATION: y = (x-1)!

NAME: Gamma (Gamma; factorial defined for all complex numbers)
FIRST SEEN: Episode 251
APPEARANCE: Hair outlines his/her graph, being pale yellow on top (above x-axis) and purple below. Purple eyes. V-necked black shirt with a pink exclamation mark, dark pants and pink combat boots. Black collar with white studs on his/her neck and a single yellow ‘gamma’ earring that s/he wears inconsistently.
KEY HISTORY: S/he was brought to High School Math by TPTB in the same way that Maud was, to observe them. S/he befriended QQuinn, hoping to find a diplomatic solution to the decimal war, and was approached by QLyn with questions about sexuality. After QSine was elected, s/he admitted to everyone that s/he was a spy - and became minister of foreign affairs in QSine’s new cabinet.

Character had no Serial counterpart.



45.
NAME: Mink (Minkowski’s ? Function)
FIRST SEEN: Episode 152
APPEARANCE: Orange hair curving up to her left in a curious pattern, between yellow earrings denoting ‘0’ and ‘1’. Red eyes, orange eyeshadow, and small red horns on her head. (Is said to resemble her cousin, “Devil’s Staircase”.) Has a button up shirt with ?s on the collar, a red sweater with green highlights and a red ? emblazoned on it, plus dark pants. Carries an umbrella with a ? handle.
KEY HISTORY: Speaks all in questions. Happened to be visiting where Logan’s gazebo crashed, along with Con. Portalled out with Con. Unclear whether she was Con’s inverse, or merely his wife.



46.
NAME: Con (Conway’s Box Function)
FIRST SEEN: Episode 152
APPEARANCE: Blue hair curving up to his left in a curious pattern. Blue eyes and a floating square box floating over his head like an angel halo. Has a button up shirt with []s on the collar, a purple sweater with blue highlights and a blue police box emblazoned on it, plus light pants. Carries a blue journal.
KEY HISTORY: Speaks all in rhyme. As the box function, he knocks Hevvi out, and alludes to Sine needing statistics if she wants probability. Opened a portal for himself and Mink. Unclear whether he was Mink’s inverse, or merely her husband.



47.
NAME: Thomae “Mae” West (Popcorn/Thomae’s Function)
FIRST SEEN: Episode 200
APPEARANCE: Wears a headscarf covering her head and neck, with the hints of Thomae’s function beneath. Blue eyes, black outfit.
KEY HISTORY: Was in Fractal City representing Lesser Used Relations on Council. Was fine with the nickname “Popcorn”, was less happy about CF visiting.


48.
NAME: Lissa Jous (Lissajous/Bowditch Curve)
FIRST SEEN: Episode 244
APPEARANCE: Pink hair that curves up, down, and around like a Lissajous Curve. Red eyes with green eyeshadow, hoop earrings, gold belt. Wears a light blue dress with another curve emblem on it.
KEY HISTORY: Runs the Jous Bar just outside the “Angle Zone”, called the “Bowditch”. Claimed to be “phasing into alternate dimensions, to escape this reality”.
CANON SIDE STORY: Lissa did escape to another reality, only to be identified by Para and recaptured by Alijda Van Vliet. The “Epsilon Project” was then going to try and undo the damage her escape caused.



49.
NAME: Sigma
FIRST SEEN: Episode 214
APPEARANCE: A small red cube, 10 cm each side. Its faces show “Capital Sigma” (sum), “Lowercase Sigma” (std dev), “Sigma squared” (variance), “Sigma cubed” (skewness), “Sigma power 4” (kurtosis) and *blank/unknown*.
KEY HISTORY: This “Union Device” was retrieved by QT from CF. It was thought to have a passcode. QT unlocked it’s stats secret, and interfaced. It turned her hair a dark pink, creating red gems on her Y-Intercept bow and Factor Fork - and allowed her to mentally consult with Sigma for probabilities. (Sigma eventually speaks in #219.) Hyper then interfaced through QT, making QT’s hair shift purple, while morphing her fork into a double crescent wand. When Hyper unions alone with Sigma, she also has access to that wand, and Sigma turns Hyper’s hair blonde and her accessories purple.



*THE UNSEEN*


50.
NAME: TPTB (Transcendental Pi-Type Beings)
FIRST REFERENCE: Episode 125
APPEARANCE: Unknown
KEY HISTORY: TPTB were only fully named and described as those “externally influencing our world” by Cosecant (#137), but they seemed to be who Maud was speaking with in Episode 97. Para had some sense of them when she almost died, falling off the cliff, but it didn’t coalesce until #210, identifying their Personal Deity as “Taylor” (hence Taylor’s Polynomials). Elly said the “new order” (comic) had “Q” as a deity (hence Any Not-Qs). Tangent suggested that TPTB could not interfere directly, hence Q manipulating Taylor’s Polynomials into destroying themselves, except unification occurred instead... that has never been confirmed.
AUTHOR ASIDE: Yeah, totally a reference to the author, and to “The Powers That Be” (TPTB) from the Buffyverse, but at this point what HASN’T influenced this quirky tale...

50.
NAME: Norm (Statistics)
FIRST SEEN: Episode 182
APPEARANCE: Unknown
KEY HISTORY: He walked into the Overline Bar, grousing about people thinking a fourth quartile existed. His features would not resolve into a face.
CANON SIDE STORY: Statistics became increasingly angry and erratic, owing to the actions of humans, even managing to bend reality and appear (hidden in a cloak) within the Hilbert Curve where Sine was trapped. Rosemary Thorne helped Statistics to calm down and reconcile with those in Fractal City.

51.
NAME: CF (Characteristic Function)
FIRST SEEN: Episode 206
APPEARANCE: Unknown
KEY HISTORY: Described by Mae as a “freaky person”. Was present but unseen/invisible in a small novelties shop visited by Logan and QT. Told them whatever they took would decide their path, then as QT decided, CF directed Logan to a book that would describe the sizing of an infinite set. Logan was naturally hesitant.



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