One of the sources of inspiration was the observation that on a beach, even one with little surf like Lake Superior in August, you can see traces in the sand of the farthest advance of every wave. It is only a tiny ridge 1-2 mm high, but you can see it. And as each successive wave comes it erases all previous traces and leaves its own. This leaves a tracery of fine random curves which merge and overlap. Could one create such a pattern by computation?

Each wave trace is "one-dimensional" noise. Noise which can be graphed as some waveform versus distance x.

Noise is much studied in a number of scientific disciplines. One of the most thoroughly studied forms is electrical noise, because it is a major factor in communication systems.

The big difference between one form of noise and another is its frequency spectrum (assuming we are talking about time-dependent noise). This relates to how the noise energy is distributed over frequencies. The most basic form of noise is "bandwidth-limited white noise" in which the noise all lies between two particular frequencies and the noise energy is the same at all frequencies. Fundamental theories show how this kind of electrical noise is related to the atomic nature of matter. It is very common. As an image, where one graphs such a noise waveform as y(t) versus x, this noise tends to be rather boring. One mostly sees only the highest-frequency components.

In computer-generated art one of my objectives is to create images which have interesting "features" at all length scales. If one only sees the short wavelengths, one can hope to improve this by setting up a frequency spectrum such that the noise power is lower at high frequencies. Noise of this kind also turns out to be fairly common and has a sizable literature under the name of "1/f noise". Here the average noise amplitude decreases with frequency as an inverse power law: amplitude ~ 1/f^n where n is a dimensionless number which is often measured to be close to 1 in practical cases.

A noise drawing routine was set up, with the average amplitude varying as a negative power of (1/wavelength). This power exponent was made variable and adjusted for a "pleasing" shape. Interestingly, images which showed visually perceptible features "at all wavelengths" had an exponent around 1.

In "The Self-Made Tapestry, Pattern Formation in Nature" by Philip Ball he notes that classical music, rock music, and conversation all have an approximate 1/f frequency spectrum if analyzed with noise-measuring instruments. There is something basically appealing about 1/f noise in the sound domain.

After some experimentation, images were created by finding successive random "1/f" waves, and coloring the region above this wave a particular color. The baseline of the wave was shifted upward for each new wave, which then over-writes what existed before. This gives a sort of abstract landscape. The thought came to use alternating blue and white colors in the upper part of the picture as a sky.

Most people find that the eye recognizes image(s) 23 as a sort of mountain landscape. It is rather abstract, and I think may be about at the limit of what the senses recognize as a landform. If the blue-and-white "sky" is omitted, people tend to see it as largely abstract.