Non-linear iterated function systems and the creation of fractal patterns over regular polygons

Loocke, Philip Van

doi:10.1016/j.cag.2009.05.003

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…Based on the linear complex mapping, a type of nonlinear complex mapping families are studied in [6] to form the condition of an iterated function systems, and the relationship of the initial point selection and the generated attractor is discussed. Combine the linear affine transformation and square root function, the literature [7] provides the method of drawing fractal graphics when the initiator is regular polygons or circles. The representation form based on polynomial transformation in [8] is applied to draw the fractal graphics, increasing the diversity of fractal attractors.…”

Section: Introductionmentioning

confidence: 99%

A Synthesis Method of Nonlinear Transformation and Affine Transformation for Constructing NIFS

Liu¹,

Zhu²

2018

Proceedings of the 2018 International Conference on Mechanical, Electronic, Control and Automation Engineering (MECAE 2018)

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In order to construct a large number of diverse and innovative fractal graphics, an arbitrary nonlinear transformation of V(x,y) is introduced into the classical iterated function systems to change the construction form of nonlinear iterated function systems (NIFS). The deterministic algorithm and random iteration algorithm are used to draw the fractal graphics. The summarization of relevant transformation rules are obtained according to the generation of NIFS attractors. The experimental results show that the combination of nonlinear transformation and affine transformation enriches the transformation types of iterated function systems, and a simple and effective approach is provided for the drawing of NIFS fractal graphics. And, the novel structural fractal mountains and the fractal graphics with D n+1 、Z n+1 symmetrical

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Section: Introductionmentioning

confidence: 99%

A Synthesis Method of Nonlinear Transformation and Affine Transformation for Constructing NIFS

Liu¹,

Zhu²

2018

Proceedings of the 2018 International Conference on Mechanical, Electronic, Control and Automation Engineering (MECAE 2018)

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“…As in Loocke's method [13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped.…”

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confidence: 99%

Creation of Fractal Images with Rotational Symmetry Based on Julia Set

Han

2014

JKGS

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We studied the creation of fractal images with polygonal rotation symmetry. As in Loocke's method [13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped. Also we can improve fractal images by modifying probabilistic IFS algorithm, and we suggest a method of deforming Julia set by changing exponent value.

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