Artificial neural net attractors

ÐAesthetically appealing patterns are produced by the dynamical behavior of arti®cial neural networks with randomly chosen connection strengths. These feed-forward networks have a single hidden layer of neurons and a single output, which is fed back to the input to produce a scalar time series that is always bounded and often chaotic. Sample attractors are shown and simple computer code is provided to encourage experimentation. # 1998 Published by Elsevier Science Ltd. All rights reserved Dynamical systems modeled by nonlinear maps and ̄ows can produce an astonishing variety of aesthetically appealing visual forms [1]. One such nonlinear map is an arti®cial neural network [2]. Neural networks o€er a number of advantages as generators of interesting visual patterns: 1. Their outputs are automatically bounded with the proper choice of a squashing function. 2. Neural networks are universal approximators [3] and hence are capable of generating any pattern if they are suciently complicated. 3. There is a large literature on the design, training, and behavior of neural networks. 4. Neural networks mimic the operation of the human brain, and hence they are a natural choice for emulating human-generated art. 5. In principle, they can be trained to improve the quality of their art, just as a human can be trained. There are many possible neural network architectures. The one used here is the feed-forward network shown in Fig. 1. It has an input layer with D elements (y1, y2, . . . ,yD) a hidden layer of N neurons (x1, x2, . . .xN), and a single output y0. The network is characterized by the equations: xi ˆ tanh XD