1.G. The Random IFS Algorithm

Definition and Illustration of the Random IFS Algorithm

Start with a point (x₀, y₀) belonging to the fractal.

For example, take (x₀, y₀) the fixed point of one of the T_i.

Let {n₁, n₂, ... } be a random sequence of numbers, each from {1, ..., N}. (In Same Picture we'll say why random is important.)

Generate a sequence of points

(x1, y1) = Tn1(x0, y0),

(x2, y2) = Tn2(x1, y1),

...

We shall see this sequence of points eventually will fill up the fractal to any prescribed accuracy. For example, here are pictures of the Random Algorithm applied to the gasket rules.

The left picture shows 500 points, the right 5000.

Return to the Random IFS Algorithm.