Theatre Design & Technology - Spring 1992 - 19

CHAOS
hen I was firsr asked ro generare some images for rhis
arricle, my knowledge of
fracrals was exrremely limi red and my
knowledge of complex formula or compurer programming even less. So I
marched off ro rhe local public domain
srore rhar specialized in sofrware for my
compurer and in abour ren minures
walked our wirh rhree disks crammed full
of programs for generaring fracrals. Toral
cosr: 512 (54 per disk ro cover rhe cosr of
rhe disk and copying rhe sofrware).
I figured I would go home and generare a few images, if rhe sofrware worked
(I mean, how good could free sofrware
be') and rhar would be ir. Well, ir is now
rhree monrhs larer and I am hooked. I
have sar for hours in fronr of rhe compurer moniror warching some of rhe moS(
inrricare and brearhraking images I've
ever seen being creared before my eyes.
The possibiliries indeed seem endless (as
I'm sure a marhemarical rheorerician
could have rold me). Change jusr one
paramerer in rhe formula or adjusr rhe
number of irerarions (rhe number of
rimes rhe formula is repeared) and an
enrirely new and wonderful image will
appear.
The fracral images creared are all
based on irerared complex formulas. The
mosr famous of rhese are rhe
"Mandelbror" and "Julia" formulas.
When invesrigaring a marrix of poinrs
rhe program inserrs each poinr inro rhe
formula and calculares rhe speed of divergence (rhe number of irerarions required
for rhe poinr ro escape ro infiniry). When
rhis happens, rhe formula is sropped and
rhe poinr is assigned a color based on
how many irerarions were performed. If
rhe maximum number of irerarions ser in
rhe program is reached and no divergence is derecred, rhe poi nr is colored
black. The "Mandelbror" formula creares
a very disrincrive black area surrounded
by a complex border of divergenr colors.
As you zoom in on ponions of rhe image,
you reveal rhe infinirely deep complexity
of rhar border.
You only have ro look ar rhe sheer
number of calcularions required ro generare a fracral image ro undersrand why ir
rook rhe compurer revolurion ro make ir
possible for us ro appreciare rhe beaury of
rhem. \X1hen you consider rhar mosr of
rhe images I generared were from a
marrix of 640 by 400 poinrs, you come
up wirh 256,000 numbers rhar have ro
be impured inro a complex formula.

FRACTALS

When you mulriply rhis ro, say, 100 irerarions per poinr, you wind up calcularing
rhe formula over 25 million rimes using
numbers up ro 32 decimal places long.
Even wirh a fasr personal compurer, ir
can easily rake 20 or 30 minures ro generare a single image-which isn'r roo bad
when you rhink abour whar rhe compurer has ro go rhrough.

The fracral images used in rhis arricle
were all generared from eirher shareware,
freeware or public domain sofrware wrirren for rhe Amiga compurer. This sofrware or comparable sofrware for orher
rypes of com purer are readily available
from eirher public domain or commercial sofrware developers.
The freeware program used ro generare rhe Mandelbror formula is called:

Mal1delBlitz 1.0
wri nen 12 June 1990 by
ico Francois
Corbielaan 13
B-3060 Berrem
BELGIUM
The rhree dimensional "Mandelbror"
and "Julia" images were creared by a
shareware program called MandelMO/l 11 tail/S. (Shareware is sofrware freely
disrribured. The programmer asks rhar, if
you like and use rhe program, please send
a small conrriburion, in rhis case $10.)
The program creares rhe gray area from
poinrs rhar have low divergenr rares.
When a user-derermined irerarion number is exceeded, rhe poinr is rhen colored.

MalidelMo/ll1tail/S V2.1
Marhias Orrmann
Srrindbergsrr. 5
0-8000 Munich 60
GEIUvIANY
All rhe orher images were creared from a
mulripurpose public domain program
called Fractals. Some of rhe formulas used
are: Lambda COS (Z); BIOMORPH
(based on rhe same principle as Julia sers
bur differenr formulas);
ewronRaphson (merhod of finding roors ro a
funcrion); and Epsilon SIN (Z).

Fractals
Ronnie Johansson
Hasselkulleg. 70
461 62 Trollenan
SWEDEN

FOUR FRACTAL IMAGES
GENERATED BY THE
"MANDELBROT" FORMULA
ZOOM INTO THE INFINITE
COMPLEXITY OF
"SPACE."

All of rhese programs can be found in rhe
Fred Fish "Freely Redisrriburable
Sofrware Library":
Fred Fish
Amiga Library Disks
1835 Easr Belmonr Drive
Tempe, AZ 85284
-Perer Nordyke

Sail Diego State Ulliversif]/
TD&T

1992SPRING

Table of Contents for the Digital Edition of Theatre Design & Technology - Spring 1992