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maths and butterflies

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What level are you at?
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Does it have to be about biological butterflies? Because there are several mathematical objects and concepts named for butterflies: the butterfly theorem in geometry, the butterfly graph crops up quite a bit in graph theory, the butterfly effect of course.

If it must be about butterflies, you could look up Turing patterns and butterflies. It's probably about the same level or harder than fractals, but there may be something there.
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You could talk about symmetry, since the wing patterns are symmetric.

Intro group theory is a really nice subject, and pretty accessible.
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Maybe Interference of waves underlying structural color.. or sensitivity to initial conditions in chaotic systems implying its wing flaps leading to hurricane?
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Morphogenesis of wing colour patterns.  I've not seen that done for butterflies and the differences with other patterned organisms might be interesting.
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[removed]
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Not necessarily about butterflies, but perhaps about the butterfly effect and the statistics surrounding various outcomes of the initial action which started the chain reaction, could even delve further into creating simulation software with different interactive starting conditions, again noting the relevant statistics/maths behind it all.

(I am pre-undergrad so apologies if that isn’t a great idea)

Edit: this could also evolve into chaos theory during the latter stages of the butterfly effect
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Escher has used butterflies in some of his tessellations.
by

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