[Fwd: Painting by numbers: Fractal art produces pictures worth 1,000 equations]

[Roger Bagula]

This didn't get through on the first post...

-------- Original Message --------

Subject:	Painting by numbers: Fractal art produces pictures worth 1,000 equations
Date:	Sun, 31 Dec 2006 06:37:36 -0800
From:	Roger Bagula <rlba...@sbcglobal.net>
Newsgroups:	sci.fractals,sci.nonlinear,alt.fractalks

( I recognize the author of the article : Scott La Fee has bee writing 
for Copley News Service/ San Diego Union since the 1980's.)

http://www.bendweekly.com/news/1601.html
Dec 29,2006
Painting by numbers: Fractal art produces pictures worth 1,000 equations
by Scott LaFee
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Fractals are like metaphysical Legos, building blocks that connect the 
worlds of number and shape. But unlike the plastic toy bricks, you can't 
see fractals, which are essentially algorithms or mathematical rules. 
Instead, you see the patterns they produce, which are fundamentally 
distinctive, to say the least.

All fractal patterns share a few common traits.



FRACTAL ART - “Warm Glow” is the product of a Mandelbrot set, perhaps 
the most famous fractal. Coloration is based upon how many times each 
pixel in the image was “visited” during repeating equations. CNS Photo 
courtesy of Kerry Mitchell.
Each is self-similar. That is, the whole and the parts of the whole 
share a resemblance, regardless of scale. This rule isn't always 
obvious. Sometimes fractals can be self-similar only in a statistical sense.

Each is recursive: the underlying math repeats again and again.

Each evokes a sense of nature. Indeed, nature abounds with examples of 
fractals: branching rivers and blood vessels, swirling cloud systems, 
the repeating patterns of mountain ranges and the rocks that comprise them.

People have long looked at these patterns and been fascinated, but it 
was not until the 1960s, when computers became sufficiently powerful, 
that mathematicians, scientists and engineers began to create and 
investigate fractals in their infinite detail.

It's been a fruitful endeavor. Fractal science allows researchers to 
perceive order in apparent disorder. Fractal concepts have been used to 
analyze the distribution of galaxies in the universe, the frequencies of 
economic cycle indices and the probabilities of earthquakes and wildfires.

Along the way, fractals became art as well. Early efforts were colorful 
but relatively crude: a psychedelic paisley of spikes, spirals and 
zigzags. Today's art, like the math, has progressed. Powerful 
off-the-shelf software programs can now create remarkably exquisite 
fractal images on home computers.

Many employ a basic technique: Every pixel or point on the screen is 
assigned a unique number. Each number is inserted into a mathematical 
formula to produce a result. Each result is reinserted into the same 
formula to produce a new result. This is done again and again, a process 
called iteration. Pixels are then colored based on the mathematical 
results, whether numbers got bigger or smaller.

The computer, of course, is critical. A small fractal image may contain 
300,000 points, with each point processed through a fractal formula 
1,000 times. That's 300 million calculations. A poster-sized image could 
require 1 trillion calculations.

Massive number crunching doesn't guarantee a work of art. Indeed, 
fractal calculations often produce more white noise than mathematical 
masterpieces. That's where the artist comes in. To be successful, as 
these examples from some of today's finest fractal practitioners show, 
requires an understanding of both form and function.

Copley News Service
67 times read