Some of the most fascinating Julia sets are those that Benoit Mandlebrot referred to as "dragons." The best dragons are found in or near the bulbs with a period of five or greater at the rear of the Mandelbrot Set. The image below shows the periods of some of the bulbs. The bulbs get smaller and the periods increase until the bulbs get infinitely small and the periods infinitely large at the end of "Elephant Valley," the cusp at the rear of the Mandelbrot Set.
The number of "arms" that a dragon has is equal to the period of bulb that it is located in or near. The dragons in the image below all have eight arms because they are located near the period-eight bulb.
The image below shows the loacations of the dragons. Notice that the dragons on top of the bulb have a clockwise twist and the dragons on the bottom of the bulb have a counter-clockwise twist. Notice also that the twistedness of the dragons increases as their locations approach the root of the bulb.
The dragon below is sort of my mascot. I call him "Twister" because he loves to do the Twist. Click on him and he will dance for you.
I hope you have enjoyed this page.