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Flower Spirals by Hai-Etlik Flower Spirals by Hai-Etlik
Vi Hart's videos on spiral structures in plants got me thinking and so i put together a little Ruby program to implement this.

These flower shapes were created by rotating the "petal" by τϕ and scaling it by 0.99 then repeating 200 times. As I go I colour the petals using a repeating sequence of colours which I get by rotating the hue by τϕ (It's a convenient way to get an an easily expanded set of distinct hues with maximum contrast). The number of colours in the sequence is shown above each flower, and the number is red if it's a Fibonacci number.

Here are the videos that gave me the idea:
JohnColburn Featured By Owner Feb 7, 2012  Professional Digital Artist
What's really interesting to me is that the fibonacci ones seem to have a common property of producing the "smoothest" spirals, which is not intuitively what I would have expected. I assume that the math behind that pattern makes perfect sense to someone who knows more about this sort of rotational algorithm, but I've never been great at "pure" mathematics so it's kind of mysterious to me ^^.
Hai-Etlik Featured By Owner Feb 7, 2012
It makes sense in a way as ϕ is the limit of the ratio of consecutive Fibbonacci numbers.

1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.666666
8/5 = 1.6
13/8 = 1.625
and so on

But it's still one of those WTF moments, sort of like the first time you encounter Euler's Identity.
JohnColburn Featured By Owner Feb 9, 2012  Professional Digital Artist
Yeah, I never would have thought of that ^^. Makes sense, though.
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February 6, 2012
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