Fractal approximation of chaos game representations using recurrent iterated function systems

Martin Do Pham; Martin Do Pham

doi:10.3934/math.2019.6.1824

AIMS Mathematics

2019, Volume 5, Issue 6: 1824-1840. doi: 10.3934/math.2019.6.1824

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Fractal approximation of chaos game representations using recurrent iterated function systems

Martin Do Pham ^,

Applied Math Department, University of Waterloo, Waterloo, Ontario, Canada

Received: 01 October 2018 Accepted: 19 March 2019 Published: 20 January 2019
MSC : 37H99, 92D20

We demonstrate that chaos game representations of Cannabis sativa may be approximated by the chaos game approximation of a recurrent iterated function system attractor. Via numerical experiments, we then study the fractal scaling properties of both objects and apply a wavelet decomposition in order to investigate scale-invariant patterns. We show that the attractor of a recurrent iterated function system scales similarly to the chaos game representation and has a similar wavelet multiresolution analysis profile.
- chaos game representation,
- iterated function systems,
- multiresolution analysis,
- cannabis sativa
Citation: Martin Do Pham. Fractal approximation of chaos game representations using recurrent iterated function systems[J]. AIMS Mathematics, 2019, 5(6): 1824-1840. doi: 10.3934/math.2019.6.1824

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Abstract

We demonstrate that chaos game representations of Cannabis sativa may be approximated by the chaos game approximation of a recurrent iterated function system attractor. Via numerical experiments, we then study the fractal scaling properties of both objects and apply a wavelet decomposition in order to investigate scale-invariant patterns. We show that the attractor of a recurrent iterated function system scales similarly to the chaos game representation and has a similar wavelet multiresolution analysis profile.

References

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