Mathematical "Abstracts"

Lawrence Holbrook
Bridges: Mathematical Connections in Art, Music, and Science (1999)
Pages 21–26


"Abstract" art is derivable from mathematics in countless ways. Three techniques are discussed in this paper; two of which start with fractals generated from the iteration of almost any mathematical function. Fractals usually have observable and aesthetic properties such as symmetry and self-similarity. They also, by consequence of definition, are such that surface and perimeters appear convoluted and jagged. These patterns, of interest in themselves are the basis for more "painting-like" abstracts resulting from the incorporation of random numbers into the fractal equation or into some other controlling feature of the iteration process. Alternatively, fractals can . be softened, modified and transformed combining graphics software techniques with color map design. Finally, non-fractal images are produced non-iteratively by mathematically averaging random numbers and processing the results with graphics software.