This page discusses the behavior of a simulated evolution system by Michael Palmiter I first encountered in the 1989 Scientific American column "Computer Recreations", by A. K. Dewdney. I played with the code for this a number of times over the years and eventually produced some data analysis tools for examining the course of the simulated populations over time.

It was an interesting system to write and proved to be a good learning experience as I improved it over the years. I still find it amusing to set it running from time to time.

This page discusses the behavior or a simplified model which captures much of the behavior of a reaction-diffusion system. Stripes and spots in many configurations can be produced.

I have explored some aspects of it, but there is plenty more work which can be done on this model.

The model is mentioned once in Wolfram's big book, but he does not cite who originally developed the model. I began work on this model years before Wolfram's big book came out and I have not found other references to this model. I'm quite certain I read of it somewhere before I began working on this, but I have no recollection as to where.

Here I discuss the maths needed to calculate new fold lines in origami. The mathematical model begins with generalized definitions of points and lines, then applies origami axioms to find new points and lines. Because I was writing this into a computer simulation while I was deriving the math, I have made efforts to explain how the math can be rendered into a form usable in a general programming environment.

Primarily the axioms are based on the work of Huzita and others. The final two discussed are not commonly recognized, but were important in my work.

This project began as an attempt to write detailed instructions for folding origami models. My background in computer programming led me to develop a structured language to describe the features of the paper, the folding process, and the new features created during folding.

The language is limited to 2D models and still needs work to be entirely unambiguous. I'm writing a compiler to translate the written script into images similar to those found in a standard origami diagram.

Development of the language has often pushed forward when a problem came up in work on the compiler. The nature of programming is such that any algorithm vagaries are readily exposed.

This is the origami simulation through which the language compiler will generate its images. The maths explored earlier are fundamental to the simulation, but are entirely insufficient to produce useful results with it. I have developed and continue to develop the algorithms needed to properly simulate the folding of a piece of paper.

I don't have a proper writeup for this project yet, but the page has some examples of what the simulation can do so far.