The Game Of Chaos

A simple and accurate definition of a fractal could be: "A fractal is a geometric structure created by repeating simple patterns at different scales. These patterns can repeat in a similar or varied manner across different iterations, resulting in fractals with diverse and intricate details at various levels of scale."

The "Chaos game" is a simple method for creating fractals based on randomly selecting points and moving them on a plane. This method first defines an initial point on the plane (such as one of the vertices of a specific geometric shape), then, by repeating the following steps, a more intricate pattern is generated from the selected points:

  1. Select an initial point on the plane (e.g., one of the vertices of a specified geometric shape).
  2. Randomly select another point (e.g., vertices) from the selected points.
  3. Move the current point towards the newly selected point.
  4. Repeat steps 2 and 3 for a certain number of iterations (or indefinitely in some cases).

This method has various applications in different fields, including:

  • Modeling nature: Using the chaos game, nature and physical phenomena such as cloud formation, weather, biological structures, etc., can be modeled.
  • Artistic and design applications: By employing the chaos game, patterns and designs with unique and infinite beauty can be created for use in art and design.