Mandelbrot's Bug

  Chaos describes the way most of us see nature. It could be the shape of clouds, the profiles of mountain ranges, or the delicate patterns of crystalline snowflakes. Long ago, mathematicians had given up describing these because they seemed to possess no order.

Then along came Benoit Mandelbrot. An immigrant mathematician working for IBM, he had long been obsessed with patterns of disorganization. Problems with computer communication at IBM mirrored the patterns he saw elsewhere. He set out to bring order to chaos.

The Bug

This is a graphical representation of the Mandelbrot Set. The color at each particular point in the plane represent the level of difficulty in determining whether that point is in the set or not.

Points colored black repesents points included in the set. On the edges, it takes fewer tries to conclude that these points are outside the set; Less tries are first violet, then blue, then green, etc,etc to orange. Here, at the far reaches, we skip to light blue tones to make clear the contours of the profile.

Note how the primary shape is repeated in various incarnations. Click on the picture to see an expanded version. Even in the greatest detail, the patterns repeat.


This is the notch area between the two half’s of the bug. Once again, note how the frill is repeated in ever decreasing size. Yet the general shape is similar.


This is another view of the notch in greater detail. Here we can see the shades of blue; draker blue representing relative ease in determining that these points are outside the Mandlebrot Set. Black is clearly within the set. We color the pixel black if, after 256 passes, the orbit is still contained.



In yet greater detail, this is from the left side of the notch. Patterns continue to repeat and morph into similar shapes.


Bug Yellow

Far down one of the dragon's tendrils lies this bug in a patch of yellow.


Blue Burst

Yet farther down the tendril is this bug shaped object.


Black Witch

This is an element on one of rays emanating from the Blue Burst. No matter how far in you go, similar shapes are found.

(-.6476001475,.4791158594j), .000000375

Lace Doile

Down one of the tendriles, this is nodule on a nodule.

(+.1419059625, .6493743156), .0000003906