Art in the Digital Age:
An excursion into FRACTALS

By Herb Ranharter

Entropy, Chaos, Fractals: Patterns for ART.

Astrology can easily and perhaps rightfully be dismissed as utterly illogical nonsense. Yet it is possible to use astrology to achieve meaningful results. If understood as a set of arbitrary rules (I am paraphrasing Douglas Adams), such rules let personality traits come forth like graphite dust sprinkled on paper makes unseen imprints emerge. Useable patterns are everywhere and can be found by viewing and probing the seemingly unrelated in unconventional ways. Patterns enrich the creative process.

You are already familiar with a similar idea, the "happy accident". Activity beyond our reasons, skills and intentions. Activity that nevertheless managed to produce surprisingly attractive results. Each such accident is an incident of applied chaos, a product of chance. An event occured that could be termed spontaneous self-organization; a useful pattern has emerged. There are surprisingly many ways to conjure up such patterns. A bonanza for the creative individual.

Exhibit one:

A rubber ring rolled from a tubular carrier jumps off onto the floor. Upon examination we come to realize a remarkable transformation has taken place: the ring per chance twisted beyond its relaxed position and assumed an unexpected shape. Repeated experiments can lead to all kinds of discovery: Note: the shadows are yet another noteworthy aspect of these incidents. It should also be said that it is usually useful to view images from different vantage points (e.g. upside down etc.).

strip

Given a fine enough grid and a well chosen formula plus some strategic coloring choices the most astounding results can be obtained.

fractal
©1999 Herb Ranharter
(drawing detail)

There are a great many other ways to accomplish such incidental images. Another way would be to simply create an array of lines where every line gets varied in some manner, As the lines overlap horizontally and vertically, their intersections create cells that can then be colored in. You get the point. All of these methods have the distasteful element of being created largely by computer. How to make such arrays your own creative endeavor is the nagging question.

Exhibit two:

Another approach has to do with mathematics (yes, you may shudder if you like). Any equation that can produce a result in a coordinate system (an equation containing the terms x and y) will do. Without going into the math at all, it can be said that for every picture point in a Cartesian coordinate system two numbers (x and y) can be inserted into the chosen equation to produce a result. This result will be some kind of a number. The result would be expected to vary for each and every coordinate point and can then be made subject to arbitrary rules. For example I could decide that if the third decimal position of the result for x=3 and y=5 for the chosen formula turns out to be 7 that particular point shall be colored green. Had it turned out to be 3, I might have chosen red and so on.

grid

grid

The effect can be surprising:

fractal
©1999 Herb Ranharter

Exhibit three:

The Rules:

1) work small
2) work fast
3) allow the calculated contour to suggest a fitting image
4) work as much in a semi-trance state as possible
5) no erasing.

Mandelbrot set (a specific formula attributed to Benoit Mandelbrot) was generated in solid black and white. This was done with a fractal program called Chaos by Autodesk. A set much like the one used in the illustration above was calculated and printed in high contrast. The image was then blown up to a suitable size and placed on a light table to serve as pattern for a drawing. An arbitrary set of rules was then decided upon and used to limit the drawing.

Here is the result: ( The resolution of the drawing defies digitizing for internet-size files that load at a reasonable speed. The key lines in this drawing were made with a sharpened 0.2mm F pencil lead. The overall size is 18 inches square. It is for this reason that the detail gets somewhat lost):

fractal detail
©1999 Herb Ranharter (drawing detail)
Note: it took 75 hours to complete this drawing.


© 1999 Herb Ranharter
All Rights Reserved.

@delARTe is a pro bono contra malum organization.
©1999 @delARTe All Webrights Reserved.

Visit Herb Ranharter's home page at Art2u.


Comments?

July 3, 1999

updated September 28, 2004



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