No doubt as some people have already seen, today morning wolfram posted the best valentine ever. The graph depicting cupid with its arrow and floating hearts around it involves something like 6 pages of parametric equations. My question to this community is, does any one have any idea how these equations were discovered? Is there a methodology here when people post equations with graphs looking like bunnies or hearts or is it just playing around with trigonometric functions with a little bit of intelligent guessing until something interesting pops out? Are there an papers/books/references on these type of derivations? No doubt these have been done for a while. I hope somebody at wolfram will publish something soon.
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2See http://math.stackexchange.com/q/288690/856 and http://mathematica.stackexchange.com/q/17704/484 – Feb 14 '13 at 23:27
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Second link is really good. – zaa Feb 14 '13 at 23:39
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http://en.wikipedia.org/wiki/Spline_%28mathematics%29 and http://en.wikipedia.org/wiki/Vector_graphics
Wolfram's Cupidon was made by trigonometrical "parts". Anyway, the basic idea is the same as with polynomial splines. Take any advanced vector graphics editor (or modify or make such) - and you will get automatic derivation of such equations.
And heavy use of Heaviside Step Function in it (http://mathworld.wolfram.com/HeavisideStepFunction.html), if I'm correct, is only for masking/merging such fragmentation.
zaa
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