Non-linear transformations combinations on fractal structures and aggregates

Sancho Salcedo-Sanz; Pablo Álvarez-Couso; Luis Castelo-Sardina; Jorge Pérez-Aracil; Sancho Salcedo-Sanz; Pablo Álvarez-Couso; Luis Castelo-Sardina; Jorge Pérez-Aracil

doi:10.3934/math.2026078

AIMS Mathematics

2026, Volume 11, Issue 1: 1878-1899. doi: 10.3934/math.2026078

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Non-linear transformations combinations on fractal structures and aggregates

1.
Department of Signal Processing and Communications, Universidad de Alcalá, 20805 Alcalá de Henares, Madrid, Spain
2.
Department of Design and Image, Universidad Complutense de Madrid, 28040, Madrid, Spain

Received: 21 October 2025 Revised: 02 December 2025 Accepted: 15 December 2025 Published: 20 January 2026
MSC : 28A80, 46Txx

This paper discusses the effects of applying different non-linear transformations in combination to well-known fractal structures and aggregates, to obtain novel fractal images. Five different non-linear transformations are selected to be combined, and applied to existing aggregates, and the new fractal structures obtained are discussed. We show how different non-linear transformations effects (bending effects, diffusion effects, etc.) can be combined just by function composition processes, and their final results as new fractal images. We analyze the effects of the combination of non-linear transformations over classical fractals such as the Sierpinski triangle and Sierpinski carpet, in terms of the fractal dimension of the new structures created. Finally, we will also show the effect of the non-linear transformation on other fractal structures, such as diffusion limited aggregation and strange attractors.
- fractal images generation,
- non-linear transformations,
- transformations combination,
- fractal structures,
- fractal aggregates
Citation: Sancho Salcedo-Sanz, Pablo Álvarez-Couso, Luis Castelo-Sardina, Jorge Pérez-Aracil. Non-linear transformations combinations on fractal structures and aggregates[J]. AIMS Mathematics, 2026, 11(1): 1878-1899. doi: 10.3934/math.2026078

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Abstract

This paper discusses the effects of applying different non-linear transformations in combination to well-known fractal structures and aggregates, to obtain novel fractal images. Five different non-linear transformations are selected to be combined, and applied to existing aggregates, and the new fractal structures obtained are discussed. We show how different non-linear transformations effects (bending effects, diffusion effects, etc.) can be combined just by function composition processes, and their final results as new fractal images. We analyze the effects of the combination of non-linear transformations over classical fractals such as the Sierpinski triangle and Sierpinski carpet, in terms of the fractal dimension of the new structures created. Finally, we will also show the effect of the non-linear transformation on other fractal structures, such as diffusion limited aggregation and strange attractors.

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