Linear superposition of symmetric IFS-based attractors and fractal characterization

Abstract

"This study exploited the possibility of new fractal creation in order to increase drastically the stock number of handy fractal Images through the combination of limited base symmetric attractors' codes. The randomised play of 'chaos game' with the iterated function systems (lFS) comprising finite set of contractive affine maps coupled with simple coordinate transformation and linear superposition provide a framework for the new fractal image creation. However the fractal characterization that captures fractal image structural complexity and beauty was achieved by the implementation of optimum disk count algorithms. Comparison of the corresponding analytical and estimated fractal dimension of four symmetric base attractors are within the range of 3.2 and 7.1 percent absolute relative error. The correlation coefficient being R2=0.97. Aesthetically valuable symmetric fractal images were produced across various combinations explored with estimated fractal dimension 1.5329≤D≤ 1.8156 at transformation square window size of 2. Estimated fractal dimensions and magnitude were found to be independent of window size and number of base attractors' codes combined respectively. The findings of this study have potential applications in textile industries and general fashion design specializations.

"