If you type in "pikachu curve" or other famous fictional characters on wolfram alpha it generates a function to trace out the curve that resembles the character. See  .   Does anyone know how these curves are generated? It seems that this has been done for several characters so I doubt that they worked out the details by hand.  Related:
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How do people come up with equations of curves to draw out complex objects?  Some popular examples would include:  &amp;  .  This  explains the rationale for the batman curve nicely.  But other than trial and error, I can't see a reasonable way of drawing the much more complicated PSY curve.
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What are the mainstream techniques borrowed from algebraic geometry (or some other branch of mathematics) which are currently used in cryptography/coding theory? I've only heard about a small subset of elliptic curves and hermitian curves. I've also heard about research of hyperelliptic curves but I don't know if some software has already implemented it.  Could you mention some other branches of mathematics being strongly used in cryptography/coding theory and its state? (mainstream/in research)
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How can I make the equation for the planes of the wings of the lorenzattractor,  I know that the critical point should be used.  But I don't know how I should make this plane, the figure shows in yellow which plane I want.
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Is it possible to convert/export 2D curves to an svg?  I know you could render it to a raster image and then convert it with inkscape/potrace, but it would be nice if you could keep the splines the way they are in blender.
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Let us have a surface $X$ which satisfy the equation $\omega^3 = (z-1)(z-2)\cdots (z-8)$ It's stated in the task, that there are exactly $g$ holomorphic differentials on the curve. How can I find $g$ and construct them?  The genus $g$ of this curve (I tried to use Riemann-Hurwitz theorem)  The map $X(z,\omega) \to CP^1(\omega)$ has degree 3. and we have 8 branching points with 3 leaves at each. $\chi(Domain) = DegreeOfMap * \chi(Target) - \sum_{points}(BranchingLeaves - 1) $ $2-2g = 3 *(2) - 8*2 $ hence $ 12 = 2g$ and  $g = 6$ I know that in case of hyperelliptic curve there are $g-2$ (If i'm not mistaken) holomorphic differetials and they are of sort $\frac{z^k dz}{w}$. But the form of the curve equation was heavily used. UPD: there is a branhing point at $\infty$, because if we go around all points $ 1 \cdots 8$ at once, we get that cubic root of the right side is multiplied by $\exp{4 \pi /3}$ $2-2g = 3 *(2) - 9*2 $ hence $ 12 = 2g$ and  $g = 7$ (I hope that this is true)
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In the same spirit as :   I was able to crack the language code using tradition substitution cipher breaking techniques.  But I ended up cheating on the number/tetris symbols by looking on the Internet.  The number code is logical enough now I know it -- but I can't see how I would have arrived at it without help.  With regard to tetris shapes:      What would cause you to go down the path of associating Tetris shapes with controller inputs?
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I am wondering if there is an easy way to inset mesh that is generated from text/curves? When I convert text to mesh it generates a bunch of uneven triangles that don't inset properly. My only solution is slow and tedious and requires manually removing all but the outline edges and refilling with quads. More specifically I am trying to create an engraving of text into a mesh, and rather than a straight bool cut I need the engraved text to inset a bit. The result needs to mesh (not through a shader). Any ideas appreciated.
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What is the best way and process someone does to go about making a logo like that? I have seen people draw a logo and then use “image trace” but is that what people typically do? If they don’t use “image trace” but use the pen tool for example, how do you make it look like someone drew it? How do you get the lines to look like that? Any help would be appreciated! Thanks!
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I have been wanting to create a mobile game based on some of my favorite anime.  I want to know if using character images and names from those anime (even after giving full copyright credits and disclaimer) infringes any copyrights?  Would this come under "fair use" in the DMCA (I mean there are already so many not-so-legal sites using this "fair use" to continue running).  What are the possible things I can do for making this game? I have seen many online browser games based on anime which use images and elements from that anime, while I have also seen many games advertise themselves based on a anime but just use diffrent names for characters of that anime (sometimes modifying the character images, too).
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I'd like to know how this text gets adapted onto these 3D models. Could it be a PNG  which gets mapped. Or is this text pre planned how it would be layout onto the model? what's the method involved in this technique? Would the text layout need to be the same ratio done with a graphic editor like Photoshop or Illustrator? and have the mesh modelled in the same metric unit so the text can later fall correctly in place? All information is appreciated, unfortunately my college instructors are really lame in giving information....  Thank you.
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I am preparing a paper in the field of Computer Science.  In order to report test results, we usually run a number of tests and report the average of those tests.  For each test, we generate random data.  Because of the randomness, at some points, the results may come out not as expected.  For instance, a graph may be like:   Usually, one should explain why on points 8, 11 and 12 there is a decrease on the plot. Probably, it is because of that randomness.  Not hand-crafting all the graph, but just manipulating a few points makes the graph acceptable:   Since three weeks or so, I work my ass off and try to figure out why my resulting graph looks like the first one. Sometimes I feel like yielding to temptation and just modify the raw data before I go crazy.  I believe, at this point the title became misleading, so let me make it clear:  I am not seeking an advice on data manipulation. I will not manipulate my data. However, I ask to myself "how the hell this can be detected?"  And now, I don't only ask to myself, but to whole community. How is this detected? For editors, referees out there, have you ever detected something like this?
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I am using Paint to draw some swords for a character I have. I am not very experienced and this is my first time trying to draw swords.  My question is how large (Preferably in pixels) do I need to make the picture to make the curves on the sword to look smooth. I am using current scale of 100 pixels = an inch. For the first sword I made this worked fine as there were few curves and they were small but the one I am working on now have a larger curve. (A good reference is .)   EDIT: I only have access to paint. I would use other programs if I could.
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Let's get technical here. Have you ever seen Pikachu excrete? What about Charizard? Or Greninja? No! Well, I don't think anyone has. Is that a sign of them not being actual animals? Let's recall the seven vital characteristics for life: .    Movement Respiratory Sensitivity Growth Reproduction Excretion Nutrition   We've seen Pikachu move (obviously), breathe, touch, and eat.  Does Pikachu grow? Does he excrete?  I am missing one thing out here: reproduction. But we all know Pokémon reproduce, if not by normal means.   Throughout the series, we haven't seen Pikachu grow at all, or other Pokémon. Does evolving count?  We've never seen a Pokémon excrete.   Therefore, can we say they are animals?  Let me make it clear that this is only out of interest, and I have not gone basukas!
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Usually when I plot in , it always draws on the same figure. How do I make it draw in a new figure?   I know it is pretty elementary, but I'm not finding it using Google Search.
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At some point (not right away), I'll be wanting to make a character model which has multicolor hair.  Namely, it will be one color closer to the roots, and another color closer to the tips.  Is there any way to do this in blender?  I would be using Cycles for this.
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Suppose $N$ points ($(x_1,y_1), (x_2,y_2), ... (x_N,y_N)$) are given from a curve $y=\sin(ax+b)$ where $a, b$ values are unknown. Before giving these $N$ points to you, $y$ coordinate of one point is randomly tampered so that it does not lie on the curve.  Write a program to determine which point among $N$ points is NOT on the sinusoidal curve, whose $a$, $b$ values are unknown.  Any logic on how to approach this question, would be highly appreciate would be very thankful!
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I'm working on creating a half-elf paladin character for a Pathfinder game.  Full disclosure: this is the first time I've tried creating a character; I've used ones other people created before.  In the text, it mentions something about "favored classes" I believe.  What is this?