Orbit of zero for Mandelbrot-To visualize the Mandelbrot set
- Vincent Pantaloni
Drag point A (in white) to see the orbit of 0 under the Mandelbrot transformation. , so , and and so on. The different connected points show the successive of the sequence. The Mandelbrot set (in black) is the set of points A such that this sequence is bounded. http://prof.pantaloni.free.fr/
- Check the periodic orbits around the frontier in the numerous bulbs of the Mandelbrot set.
- Observe how a cycle doubles its period when passing from one bulb to a sub-bulb.
- You can assign a specific value to A by typing A=(0.2,0.3) in the input bar.