- The current point z is mapped to z2+c with the key f. Set c or z by clicking into the corresponding window, enter its coordinates after hitting c or z, or move it with the arrow keys. To specify the plane you are working in, use z or c as well, or left-click once into the inactive plane.
- Zoom in at the current point with the key i. When the “fractal” shape turns into a smooth band, increase the number of iterations with the key n. Zoom out with o and restart with h.
- To draw an external ray in the current plane, hit e and enter the angle as a fraction.
- Hit the key r to renormalize in the current plane. Specify a preperiod to mark embedded Julia sets.
- Find special parameters c or points z with the key x. The (pre-)period is remembered for the following scaling commands.
- Hit p to rescale the dynamic plane according to local similarity or asymptotic similarity.
- Hit t to illustrate asymptotic self-similarity by rescaling the parameter plane. Choose various levels with the keys 0, 1, 2, 3, m.
To do: implement x e p t 0 1 2 3 m.
Mathematical explanations under construction ...