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Now showing 1 - 3 of 3
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    Biom orphs: Computer Displays of Biological Forms Generated from Mathematical Feedback Loops
    (Blackwell Publishing Ltd and the Eurographics Association, 1986) Pickover, C.A.
    A computer graphics algorithm is used to create complicated forms resembling invertebrate organisms. These natural morphologies are generated through the iteration of mathematical transformations. Several illustrations are chosen as examples of the diversity of biological structures which result from this technique.
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    Graphics, Bifurcation, Order and Chaos
    (Blackwell Publishing Ltd and the Eurographics Association, 1987) Pickover, C.A.
    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 Xt+1=??Xt [1+Xt] -?, where ?= 1 or ?=e-Xi, 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.
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    A Monte Carlo Approach for ? Placement in Fractal-Dimension Calculations for Waveform Graphs
    (Blackwell Publishing Ltd and the Eurographics Association, 1986) Pickover, C.A.
    Many diverse and complicated objects of nature and math possess the quality of self-similarity, and algorithms which produce self-similar shapes provide a way for computer graphics to represent natural structures. For a variety of studies in signal processing and shape-characterization, it is useful to compare the structures of many different "objects". Unfortunately, large amounts of computer time are needed as prerequisite for rigorous self-similarity characterization and comparison. The present paper describes a fast computer technique for the characterization of self-similar shapes and signals based upon Monte Carlo methods. The algorithm is specifically designed for digitized input (e.g. pictures, acoustic waveforms, analytic functions) where the self-similarity is not obvious from visual inspection of just a few sample magnifications. A speech waveform graph is used as an example, and additional graphics are included as a visual aid for conceptualizing the Monte Carlo process when applied to speech waveforms.