1.G. The Random IFS Algorithm

Given IFS rules, the Deterministic Algorithm renders a picture of the fractal by

1. applying all the rules to any (compact) initial picture,

2. then applying all the rules to the resulting picture,

3. and continuing this process.

Regardless of the starting shape, this sequence of pictures converges to a unique limiting shape, the only (compact) set invariant under simultaneous application of all the rules.

The Random Algorithm is another method of rendering the fractal determined by a given set of rules, T₁, ..., T_N. In this section we explore this method for producing fractals.

Definition and illustration of the random algorithm

This leads to the question What is random?

To understand why the Random and Deterministic algorithms generate the same pictures, we also need to understand the notion of the address of parts of a fractal.

Now we can show why the Random and Deterministic algorithms generate the same picture.

The role of probability in the Random algorithm, including how to calculate it from the IFS parameters.