Fractal Home
Collection of Simple Iterations
Here we use an Iteration Machine with a single function. The calculation starts with a point P (x; y) of the two-dimensional plane. The next point is calculated with a simple formula in two variables x and y. After that, we take the result P' (x'; y') and use it for the following calculation. This iteration is repeated until the plotted points build the attractor of the process. Look for examples at the following pages.
Kaneko Attractor Machine
\[
x_{n+1} = a \, x_n + (1-a)\cdot \, \bigl( 1 - b \, y_n^2 \bigr), \quad y_{n+1} = x_n
\]
This is the iteration formula for Type I. For Type II change $y^2$ to $|y|$.
Use the Kaneko machine by changing the parameter slides at the bottom of
the attractor canvas. The new figure is drawn immediately. The figures depend sensitively
on the numerals behind the decimal point. Hint: Use -1 < A < 1 and B near 1.
The color is changed every 10000 dots, until the 10 predefined colors are used, then the colors are repeated.