I wanted to see if a maze could be generated on a grid that is not made of rectangles, but instead of various interlaced polygons. In two dimensions, of course, triangles and hexagons are the only geometries that make sense.

Here is a solution for displaying nested data in a tree-like structure *n*-levels deep. Regardless of how deep the nesting is to go, only one flat table is needed. Suppose, for example, there is a table of "groups," where a group can belong to any other group, nested as deeply as is wanted. The desired output would need to clearly show the relationships, for example:

While building a ruby on rails project, I needed to generate "seed data" to populate what will be a table of people's names. But, I wanted my sample page to look as normal as possible, so using the same name over and over, or just generating random characters would not be ideal. I wanted names that, although humorous, would look like real names and actually be pronounceable. This novel little script is a perfect example of why Ruby is quickly becoming my language of choice.

The next step I'm taking on fractal trees is to transform my algorithm from two into three dimensions. In theory, this is very simple, but implementing it, as I discovered, is a little tricky. The basic idea remains exactly the same as for the two-dimensional tree. The only difference is, that when a child branch is born from its parent, it doesn't just choose one angle, it chooses a three-dimensional vector. All of the branching and recursion work exactly the same way. The same golden ratio I used before will still be used, meaning that every size is related to every other size by a factor of $\frac{1+\sqrt{5}}{2}$.

Fractals appear everywhere in nature. They are probably most obvious in the pattern by which trees and other plants grow. I want to eventually generate entire forests and landscapes based on chaos. Before I can do that, I need to make a sort of language or library of code to render each specific element. I'll start by figuring out how to draw a fractal tree.

- Maze generation on n-sided polygon grids
- Recipe: recursive self-referential structure in rails
- Pronounceable name generation in ruby
- Fractal Trees, part. 2: three dimensions
- Fractal trees, part 1

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