FRACTAL FORMS: Coastline, generated with XaoS, a kind of computer spaceship
one can fly through fractal space, and then make snapshots of patterns
that catch one's fancy along the way.

On the road in the Northwest of America.

Fractals as Patterns of Rhythmic Movement . . .

Fractals are the discovery of the convivial and brilliant French
mathematician, Benoit Mandelbrot. Mandelbrot noticed already
when he was a young student that he had a unique ability to
solve equations visualizing them in his mind's eye as pictures.
Later, this gift became essential in his quest for a new geometry,
one not based on the simple squares and triangles of Euclidian
textbooks, that could more accurately describe the complex forms
of nature. Complex forms, like snowflakes, the double spirals
of pinecones or cauliflowers, the serptentine flowforms of rivers,
or the pattens we see pass by everyday in the skies above. Indeed,
one of his favorite sayings is, "Clouds are not spheres."

Whereas the details of the formal mathematics upon which
fractals are based are beyond me, I greatly enjoy looking at
them as a kind of meditation on form. I experience fractals like
I do all natural form, not as static shapes, but rather as complex
composites of rhythmic movements. In other words, I experience
them as a kind of music.

The three key generative principles of fractals are amazingly
simple. In my own words, they are: (1) self-similar patterns
(2) manifested at differences of scale (3) by means of an,
in theory, infinite number of rhythmic repetitions or iterative

Music indeed! And, of course, because of the in principle unlimited
number of steps involved in their generation, we need computers
to make them visible to us. That is, or we can just go outside and
study the shapes of flowers, of ice crystals, or of clouds overhead!

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Photograph by Cliff Crego © 2007
(created: XII.16.2007)