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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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marked as duplicate by Rahul, Henry T. Horton, Asaf Karagila, Ayman Hourieh, amWhy Feb 15 '13 at 3:13

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Second link is really good. – zaarcis Feb 14 '13 at 23:39

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up vote 1 down vote accepted and

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 (, if I'm correct, is only for masking/merging such fragmentation.

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