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# INTRODUCTION

In their introduction to Kolmogorov complexity, Li and Vitányi write:

We are to admit no more causes of natural things (as we are told by Newton) than such as are both true and sufficient to explain their appearances. This central theme is basic to the pursuit of science, and goes back to the principle known as Occam's razor: ``if presented with a choice between indifferent alternatives, then one ought to select the simplest one'' [1]. Unconsciously or explicitly, informal application of this principle in science and mathematics abound.

The principle of Occam's razor is not only relevant to science and mathematics, but to fine arts as well. Some artists consciously prefer ``simple" art by claiming: ``art is the art of omission." Furthermore, many famous works of art were either consciously or unconsciously designed to exhibit regularities that intuitively simplify them. For instance, every stylistic repetition and every symmetry in a painting allows one part of the painting to be described in terms of its other parts. Intuitively, redundancy of this kind helps to shorten the length of the description of the whole painting, thus making it simple in a certain sense.

It is possible to formalize the intuitive notions of ``simplicity" and ``complexity." Appropriate mathematical tools are provided by the theory of Kolmogorov complexity (or algorithmic complexity) [2]. The Kolmogorov complexity of some computable object is essentially the length (measured in number of bits) of the shortest algorithm that can be used to compute it. The shorter the algorithm, the simpler the object [3].

In this paper, I use basic concepts from the theory of algorithmic complexity to serve as ingredients for a novel form of simple art that I call ``low-complexity art." Although the focus in this article will be on black-and-white cartoons, the basic ideas are not limited to this type of application.

Next: BASIC CONCEPTS Up: LOW-COMPLEXITY ART Previous: LOW-COMPLEXITY ART
Juergen Schmidhuber
1998-06-04

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