Biom orphs: Computer Displays of Biological Forms Generated from Mathematical Feedback Loops

Pickover, Clifford A.

doi:10.1111/j.1467-8659.1986.tb00317.x

Cited by 48 publications

(20 citation statements)

References 6 publications

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“…In 1986 Pickover [23] introduced biomorphs (biological morphologies). He discovered them accidentally while writing a program for drawing approximation of the Julia set.…”

Section: Julia Sets and Biomorphsmentioning

confidence: 99%

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Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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The aim of this paper is to present some modifications of the biomorphs generation algorithm introduced by Pickover in 1986. A biomorph stands for biological morphologies. It is obtained by a modified Julia set generation algorithm. The biomorph algorithm can be used in the creation of diverse and complicated forms resembling invertebrate organisms. In this paper the modifications of the biomorph algorithm in two directions are proposed. The first one uses different types of iterations (Picard, Mann, Ishikawa). The second one uses a sequence of parameters instead of one fixed parameter used in the original biomorph algorithm. Biomorphs generated by the modified algorithm are essentially different in comparison to those obtained by the standard biomorph algorithm, i.e., the algorithm with Picard iteration and one fixed constant.

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“…In 1986 Pickover [23] introduced biomorphs (biological morphologies). He discovered them accidentally while writing a program for drawing approximation of the Julia set.…”

Section: Julia Sets and Biomorphsmentioning

confidence: 99%

“…In 1986 Pickover introduced biomorphs [23] -a modification of the Julia sets. Biomorphs were found accidentally as a programming bug [12].…”

Section: Introductionmentioning

confidence: 99%

Biomorphs via modified iterations

Gdawiec¹,

Kotarski²,

Lisowska³

2016

J. Nonlinear Sci. Appl.

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“…8) is non-linear, using complex variables and parameters. Well-known fractals out of this class are the Mandelbrot and Julia sets (see: [22] , [21] , [27] , [28] ).…”

Section: 3mentioning

confidence: 99%

Fractals (Mathematics, Programming and Applications)

Lauwerier¹,

Kaandorp²

1988

Advances in Computer Graphics III

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This tutorial will consist of three subjects. The first subject is the mathematics of fractals, several classes of fractals (Cantor sets, Koch's curve, Levy's curve, Mandelbrot and Julia sets) are discussed together with self-similarity and fractal dimension. The second subject is the generation of fractal objects, in which several methods are discussed for creating fractals (formal languages, Iterated Function Systems, geometric construction of fractals, non-linear complex mappings). The last subject is the application of fractals for modelling objects from nature. In this subject the estimation of the fractal dimension and simulation of objects from nature are discussed.

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“…"Biomorph" is the name that Clifford A. Pickover [7,8] gave to the shapes he discovered as a result of a programming bug when studying fractal properties of several complex functions. They can be considered as a particular case of Julia sets, with a divergence condition slightly different.…”

Section: Pickover's Biomorphsmentioning

confidence: 99%

Complex systems in APL

Alfonseca

Ortega

Cruz³

2002

SIGAPL APL Quote Quad

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Esta es la versión de autor del artículo publicado en: This is an author produced version of a paper published in: Marina de la CruzCIEMAT e-mail: marina@ciemat.es AbstractWe have been working for several years on the representation, study and simulation of complex systems by means of formal methods. APL2 and other programming languages have been used to develop our tools and experiments. This paper summarizes our APL2 works on fractal sets, automatic programming of cellular automata and simulation of multi agent systems .

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Biom orphs: Computer Displays of Biological Forms Generated from Mathematical Feedback Loops

Cited by 48 publications

References 6 publications

Biomorphs via modified iterations

Biomorphs via modified iterations

Fractals (Mathematics, Programming and Applications)

Complex systems in APL

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