Fractal patterns related to dividing coins

Periodic Fractal Patterns

We present an algorithm that can create patterns that are locally fractal in nature, but repeat in two independent directions in the Euclidean plane — in other word “wallpaper patterns”. The goal of the algorithm is to randomly place progressively smaller copies of a basic sub-pattern or motif within a fundamental region for one of the 17 wallpaper groups. This is done in such a way as to compl...

Artistic Fractal Patterns

We describe a flexible algorithm that can create many different kinds of aesthetic fractal patterns. The main idea of the algorithm is to randomly place progressively smaller copies of a motif within a region, thus producing a fractal pattern. This has been found to work for a wide variety of shapes for both the motif and the enclosing region. We show a several examples. If the region is a fund...

Fractal Patterns in Reasoning

This paper is the third and final one in a sequence of three. All three papers emphasize that a proposition can be justified by an infinite regress, on condition that epistemic justification is interpreted probabilistically. The first two papers showed this for one-dimensional chains and for one-dimensional loops of propositions, each proposition being justified probabilistically by its precurs...

Fractal Wallpaper Patterns

In the past we presented an algorithm that can fill a region with an infinite sequence of randomly placed and progressively smaller shapes, producing a fractal pattern. In this paper we extend that algorithm to fill rectangles and triangles that tile the plane, which yields wallpaper patterns that are locally fractal in nature. This produces artistic patterns which have a pleasing combination o...

Fractal Compression Related Topic