Abstract

Fractals have been used successfully to describe complex, irregular natural forms such as clouds, coastlines, trees, and mountains, which are difficult to characterize in terms of continuous, differentiable functions.¹ One of the most important properties of fractals is their self-similarity. As the spatial scale of viewing changes over many orders of magnitude, the fractal remains similar in structure and appearance. The Burt pyramid² decomposes an image into a sum of octave width spatial frequency bands plus a low-pass filtered component. Local spatial information is also preserved. If an inherently self-similar fractal is represented in pyramid form, one would expect each spatial band to look similar to the others. Conversely, if similar patterns are entered into each spatial band of a pyramid, the sum should be a self-similar fractallike texture. We have used this technique to generate realistic looking textures including clouds, water waves, galaxies, woodgrain, and rock. The time required to synthesize a fractallike texture is much reduced over present methods, suggesting that this method may be useful for computer artwork and animation. A real-time animation sequence of clouds and waves is shown. This sequence was produced on a DeAnza image processor driven by a PDP-11/24.

© 1985 Optical Society of America