A Perceptual Examination of the Mandelbrot Set
In these pages I’m emphasizing how I’ve explored the Mandelbrot set experientially — by looking at it and noticing the patterns. I’ve included the math in places where it’s necessary or interesting.
The Mandelbrot Set is commonly thought of as the graphic:
But that graphic is actually just a graphical rendering of the mathematical definition of the Set.
Here’s an excellent resource on the Mandelbrot Set, illustrated by just such graphics. Understanding what it teaches will aid enormously in your understanding of this site.
https://math.bu.edu/DYSYS/FRACGEOM/FRACGEOM.html
Looking at the Mandelbrot Set graphic, one notices that it comprises two basic parts:
• The Cardioid
• The train of buds (or bulbs) around its periphery
(The cardioid is the pac-man-like geometric figure that takes up most of the graphic.)
All of the buds have a base circle that is attached to the cardioid, and a flower-like set of “antennae” on a stalk sticking up from it (or from the infinite series of ever-smaller circles proceeding outward from them, if you have enough magnification to notice them).
(This set of features is less clear for the largest bud, for reasons that will become clear eventually.)
Notice that each bud’s antenna’s “flower” has a different number of “petals”.
This number is an indication of the bud’s period, an attribute that will be very useful for referring to the buds and noticing their patterns.
For more on this, continue to https://lapideos.com/mandelbrot-pattern-of-buds/