Tutorial (Mandel) | Java Applet Instructions / List of Programs

This is a variant of *Mandel*, that shows (small) pictures of the Julia sets over the Mandelbrot set. The parameters of the Julia sets are given by the centers of the squares. (I learned this way of displaying the relation between J and M by a picture in WikiPedia. )
Originally this applet is designed to illustrate the similarity between J and M near some parameters. To see this, first check "J Center: C". Then the Julia pictures are centered at the parameter values (= critical values c). next, set "J Width : 0.0" (this is an exceptional value), and "1 Julias" (oops, a grammatical exception too! :-). Finally, magnify the Mandelbrot set near -0.1010963638 + 0.956286510 i. Now you will see that the Julia set approximates the Mandelbrot set with some "rotation + magnification". This fact is rigorously justified by Tan Lei in her paper *"Similarity between the Mandelbrot set and the Julia sets"* (1990). Can you find any other parameters with this property?