" Mathematics,
rightly viewed, possesses not only truth, but supreme beauty ... a beauty
cold and austere, like that of a sculpture."
We begin our gallery tour, by
visiting a few fractals not yet discussed. These are fractals that are generally
appreciated for their looks rather then their mathematics accomplishments.
So flip through these pages and enjoy.
Benoit Mandelbrot's World
In this section we will examine
self-similar fractals originally rendered by the master Benoit Mandelbrot.
These can be found in his book The Fractal Geometry of Nature .
Figure
B.1 Fractal Umbrellas.
Figure
B.2 Fractal Canopies.
Figure
B.3 Plane-Filling Recursive Bronchi (square Trees).
Figure
B.4 Cesaro Triangle Sweep.
Inkblots of Nature.
"Natures great book is written in Mathematical symbols" -
Galileo
Many fractal shapes look strikingly
similar to shapes found in nature. We will look at some self-similar types
here.
Figure
B.5 Tempete.
Figure
B.6 Branch 2 (River gorge).
Figure
B.7 Branch 1 (Minimalist tree)
Figure
B.8 Blotch (Lungs).
Figure
B.9 Mount Fractal.
Figure
B.10 Spiny Embryo.
Fractal Potpourri
This is an odd assortment of fractals,
with interesting features. Just enjoy them, we will let you make own interpretation
of them.
Figure
B.11 Roman Scrolls.
Figure
B.12 Golden Rectangles.
Figure
B.13 Intricate I.
Figure
B.14 Intricate II.
Figure
B.15 Drunken Architecture.
Figure
B.16 Simple Coral.
Figure
B.17 Fractal Deco.
Figure
B.18 Point to Point.
We have now examined a large number
of self-similar fractal. You are at least an apprentice, and ready to venture
on your own to create your own individual style, form and structure. Your
pallet has an almost infinite range of possibilities, and who knows someday
you to might become a great master of a fractal showcase.
