logarithmic spiral tile 1

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Ignore the following if you think analysis degrades wonder:

I like this minimalistic spiral because of its extraordinarily low algorithmic information (Kolmogorov complexity). I suspect the minimal algorithm is <500 bits; mine is way longer and messy due to experimenting with resampling, and I'm not too clever.

Any algorithm that contains an iterated rotation and scaling will contain these logarithmic spirals. This means all fractals with non-zero rotation have them. Because it can be constructed from a single rotation, an isotropic scaling rule with no translation, and 2 bits [0,1], it is a kind of primitive; a basis pattern.

It is also a nice tile: its toroidally matched edges result in curves that are continuous and everywhere differentiable, excepting the two singular points.

Also see tiling variations, a short discussion of logarithmic spirals, and the MATLAB code for the basic pattern.



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