Sunday, June 11, 2017

[ewlplvow] Point growth in other spaces

The point growth fractal (coral) in the Euclidean plane (or space) is a battle between trees, which would like to branch and grow exponentially, and space, which grows only polynomially with radius.

Make the battle more severe by growing it on a (say) horizontal strip.  Cylinder also possible.  Mouse over a point to highlight the descendants.  Pick a vertical line of pixels and it highlights the most recent common ancestor.

On the other end of the spectrum, make area or volume increase exponentially also: hyperbolic space.  Conveniently, any regular polygon (pentagon or more) tiles (some) hyperbolic plane, so can be used as a pixel.  A few possibilities for hyperbolic 3-space.

Even more extreme, grow it directly on an empty infinite binary tree.  The point wanders among empty siblings or cousins, parent, or children until it occupies node with a filled parent: there are 5 possible directions of a step.  This will likely not be interesting, because there seems to be no possibility of crowding out.

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