Complex aesthetic forms that solve mathematical and cognitive problems
Inhaltsverzeichnis
Reference
Philip Van Loocke: Complex aesthetic forms that solve mathematical and cognitive problems. In: Generative Art 1999.
DOI
Abstract
A cellular method is proposed as an alternative for a connectionist approach. The present method does not use connections between cells, but introduces a field concept instead. If the fields are determined in accordance with the transformations familiar from fractal theory, then the solutions of problems that have some symmetry are forms of remarkable beauty. This way, a link is proposed between generative art and problem solving. It is conjectured that the ‘black box’ nature of connectionist systems can be replaced by an approach in which the solution of a problem coincides with a vivid visualization, also if the problems at hand are of a high-dimensional nature.
Extended Abstract
Bibtex
Used References
Bechtel, W. Abrahamsen, A. (1994), Connectionism and the mind, Oxford: Blackwell
Huizinga, J. (1966), Herfsttij der middeleeuwen Amsterdam: Bert Bakker (Translated as: The waning of the Middle Ages (1954), New York, Anchor Books),
Leshno, M. Ya Lin, V., Minkus A., Schocken, S. (1993), Multi layer feedforward networks with a nonpolynomial activation function can approximate any function, 6, 861-871
Personnaz, L., Guyon, I., Dreyfus, G., (1986), Collective computational properties of neural networks: new learning mechanisms, Physical Review A, 34, 4217- 4228
Rumelhart, D, Mc Clelland, J. (eds), Parallel Distributed Processing, 2 Volumes, Cambridge: MIT Press
Van Loocke, Ph. (1991), Study of a neural network with a meta-layer, Connection Science, 4, 367-379
Van Loocke, Ph. (1994), The dynamics of concepts, Berlin: Springer
Van Loocke, Ph. (1999a), Consciousness and the binding problem: a cellular automaton perspective, submitted
Van Loocke, Ph. (1999b), Variations of phase fields in cellular automata and aesthetic solutions for cognitive problems, in Dubois, D. (ed.), Proceedings of the 3-th congress on computing anticipatory systems, New York, American Institute of Physics Press, to appear
Yates, F. (1966), The art of memory, London: Peregrin
Links
Full Text
http://www.generativeart.com/on/cic/99/1399.htm
