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Graphics, Bifurcation, Order and Chaos
Author(s) -
Pickover C.A.
Publication year - 1987
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.1987.tb00342.x
Subject(s) - bifurcation , graphics , hierarchy , computer science , computer graphics , simple (philosophy) , chaos (operating system) , focus (optics) , class (philosophy) , theoretical computer science , computer graphics (images) , mathematics , statistical physics , artificial intelligence , nonlinear system , physics , philosophy , epistemology , optics , market economy , computer security , quantum mechanics , economics
Chaos theory involves the study of how complicated behaviour can arise in systems which are based on simple rules, and how minute changes in the input of a system can lead to large differences in the output. In this paper, bifurcation maps of the education X t+1 =αλX t [1+X t ] ‐β , where α= 1 or α=e ‐X i, are presented, and they reveal a visually striking and intricate class of patterns ranging from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. The computer‐based system presented is special in its primary focus on the fast characterization of simple “chacs equation” data using an interactive graphics system with a variety of controlling parameters.