Randomness Creates Deterministic Fractal Patterns- An Empirical Analysis of Chaos Game and Sierpinski Triangles

By Christina Zou

Takoma Park Middle School

The study first introduces how chaos game and affine transformations can generate Sierpinski triangles. It reviews the concept of the triangle address system. Through a set of selected random number generators, the research collects the results from the True-BASIC programs and performs an in-depth analysis of their address space coverage in different stages. It uses the resulting data and the generated images to discuss and compare the efficiency of the random number generators. Then, the research uses the same concept of Sierpinski triangle address space and address sequences to develop some interesting IFS, which use a pre-defined set of “forbidden” strings obtained from results of the random number generators to simulate the same images produced from the generators.