Abstract
This paper will analyse the concept and method of incursion and hyperincursion firstly applied to the Fractal Machine, an hyperincursive cellular automata with sequential computations where time plays a central role. This computation is incursive, for inclusive recursion, in the sense that an automaton is computed at the future time t+1 in function of its neighbour automata at the present and/or past time steps but also at the future time t+1. The hyperincursion is an incursion when several values can be generated at each time step. The incursive systems may be transformed to recursive ones. But the incursive inputs, defined at the future time step, cannot always be transformed to recursive inputs. This is possible by self-reference. A self-reference Fractal Machine gives rise to A non deterministic hyperincursive field rises in a self-reference Fractal Machine. This can be related to the Final Cause of Aristotle. Simulations will show the generation of fractal patterns from incursive equations with interference effects like holography. The incursion is also a tool to control systems. The Pearl-Verhulst chaotic map will be considered. Incursive stabilisation of the numerical instabilities of discrete linear and non-linear oscillators based on Lotka-Volterra equation systems will be simulated. Finally the incursive discrete diffusion equation is considered.
Preview
Unable to display preview. Download preview PDF.
References
D. M. Dubois: Total Incursive Control of Linear, Non-linear and Chaotic systems. in G. Lasker (ed.): Advances in Computer Cybernetics. Int. Inst. for Advanced Studies in Syst. Res. and Cybernetics, vol. II, 167–171 (1995)
D. M. Dubois: ContrÔle-commande incursif d'un système chaotique. Bull. de l'A.I.LG, nℴ6–7, 11–12 (1994)
D. M. Dubois: Hyperincursivity: inclusive recursivity without time arrow. Proceedings of the 13th International Congress on Cybernetics, Namur, 152–156 (1992)
D. M. Dubois: The fractal machine: the wholeness of the memory chaos. Proceedings of the 13th International Congress on Cybernetics, Namur, 147–151 (1992)
D. M. Dubois: The Fractal Machine. Presses Universitaires de Liège 1992
D. M. Dubois: The hyperincursive fractal machine as a quantum holographic brain. Communication & Cognition-Artificial Intelligence 9-4, 335–372 (1992)
D. M. Dubois (editor): Designing new Intelligent Machines (COMETT European Symposium, Liège April 1992). Communication & Cognition-Artificial Intelligence, 9–4 (1992), sequel 10-1-2 (1993)
D. M. Dubois: Mathematical fundamentals of the fractal theory of artificial intelligence. Invited paper in New Mathematical tools in artificial intelligence. Communication & Cognition — Artificial Intelligence, 8-1, 5–48 (1991)
D. M. Dubois: Fractal Algorithms for holographic Memory of inversible neural Networks. Invited paper in Issues in Connectionism: part II. Communication & Cognition Artificial Intelligence, 8-2, 137–189 (1991)
D. M. Dubois: Self-Organisation of fractal objects in XOR rule-based multilayer Networks. In EC2 (ed.): Neural Networks & their Applications, Neuro-NÎmes 90, Proceedings of the third International Workshop, 555–557 (1990)
D. M. Dubois: Le Labyrinthe de L'intelligence: de l'intelligence naturelle à l'intelligence fractale. Academia (Louvain-la-Neuve) 1990, 321 p., 2ème édition, InterEditions (Paris)/Academia 1990, 331 p, 2ème tirage, 1991
D. M. Dubois: Un modèle fractal des systèmes intelligents. In AFCET France (ed.): Actes du 1er Congrès Européen de Systémique, Tome II, 665–674, 1989
D. M. Dubois, G. Resconi: Hyperincursivity: a new mathematical theory. Presses Universitaires de Liège 1992
D. M. Dubois, G. Resconi: Advanced Research in Incursion Theory applied to Ecology, Physics and Engineering. COMETT European Lecture Notes in Incursion. Edited by A.I.Lg., Association des Ingénieurs de l'Université de Liège, D/1995/3603/01, 1995
D. M. Dubois, G. Resconi: Hyperincursive Fractal Machine beyond the Turing Machine. In Lasker (ed.): Advances in Cognitive Engineering and Knowledge-based Systems. Int. Inst. for Adv. Studies in Syst. Res. and Cybernetics, 212–216 (1994)
D. M. Dubois, G. Resconi: Introduction to hyperincursion with applications to computer science, quantum mechanics and fractal processes. Communication & Cognition — Artificial Intelligence, vol. 10, Nℴ1–2, 109–148 (1993)
D. M. Dubois, G. Resconi: Holistic Control by Incursion of Feedback Systems, Fractal Chaos and Numerical Instabilities. In R. Trappl (ed.): Cybernetics and Systems'94. World Scientific, 71–78 (1994)
A. J. Lotka: Elements of Physical Biology. William and Wilkins, Baltimore 1925
B. Mandelbrot: The Fractal Geometry of Nature. Freeman, San Francisco 1983
R. M. May: Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)
R. Pearl: Studies in human biology. William and Wilkins, Baltimore 1924
R. Rosen: Causal Structures in Brains and Machines, Int. J. Gen. Syst. 12, 107–126 (1986)
A. Rosenblueth, N. Wiener, J. Bigelow: Behavior, purpose and teleology. Philosophy of Science, 10, 18–24 (1943)
F. Scheid: Theory and Problems of Numerical Analysis. McGraw-Hill Inc. 1986
F. Varela: Autonomie et connaissance. Seuil 1989
P. F. Verhulst: Nuov. Mem. Acad. Royale, Bruxelles, 18, 1, 1845 & 20, 1, 1847
V. Volterra: LeÇon sur la théorie mathématique de la lutte pour la vie Gauthier-Villars 1931
E. von Glasersfeld: Teleology and the Concepts of Causation. In: G. Van de Vijver (ed.): Sel-organizing and Complex Systems. Philosophica 1990, 46, pp. 17–43
S. Wolfram (ed.): Theory and Application of Cellular Automata. World Scientific, Singapore/Teanek, N. Y. 1986
K. Zuse: The Computing Universe. International Journal of Theoretical Physics 21, 6/7, 589–600 (1982)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dubois, D.M. (1996). Introduction of the Aristotle's final causation in CAST concept and method of incursion and hyperincursion. In: Pichler, F., Díaz, R.M., Albrecht, R. (eds) Computer Aided Systems Theory — EUROCAST '95. EUROCAST 1995. Lecture Notes in Computer Science, vol 1030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034783
Download citation
DOI: https://doi.org/10.1007/BFb0034783
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60748-9
Online ISBN: 978-3-540-49358-7
eBook Packages: Springer Book Archive