Fractal Home
Simple Iterations
Here we look at a second example. The third one is presented in the partition Iterations II.
Kaneko Attractor Applet
Use the Kaneko machine by changing the values in the edit fields at the bottom of the applet. Press the enter button and watch the new figure. The table below shows sample values. If the figure is too big, decrease the scale factor. The radio checkboxes below choose the Kaneko square type I or the linear type II. The color is changed every 1000 dots, until the 10 predefined colors are used, then the colors are repeated.
The Formula
A | B | Dots |
Scale | Type |
|---|---|---|---|---|
0.1 | 1.67 | 30000 | 160 | I |
0.5 | 4 | 30000 | 180 | I |
0.17 | 1.3 | 30000 | 200 | II |
0.562 | 2.76 | 30000 | 250 | II |
Hint: Choose A, B > 0
Java-Codes for three machines
Get the source code of the Mira Applet
Get the source code of the Kaneko Applet
Get the source code of the Martin Applet (not shown!)
Other Orbit-Fractals
There are more similar fractals, p.e. the Gingerbreadman with a very simple iteration formula:
xn+1 = 1 - yn + |xn|
yn+1 = xn
One more example is a three-dimensional-looking fractal, although being calculated in two dimensions is the Kamtor3D.The iteration formula depends on angle functions:
xn+1 = xn * cos a + (xn* xn - yn) * sin a
yn+1 = xn * sin a - (xn * xn - yn) * cos a