Abstract
With the increasing potential of convolutional neural networks in image-related problems, we apply these methods to a fractal inverse problem: Given the attractor of a contractive iterated function system (IFS) what are the parameters that define that IFS? We create and analyze fractal databases, and use them to train various convolutional neural networks to predict these parameters. The neural network outputs produce visually different fractals, however, they could be used to create an initial population for other search algorithms. Additionally, the neural networks become increasingly accurate with increasing numbers of functions defining the IFS.
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This research was enabled in part by support provided by Compute Ontario (www.computeontario.ca) and Compute Canada (www.computecanada.ca).
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Graham, L., Demers, M. (2021). Applying Neural Networks to a Fractal Inverse Problem. In: Kilgour, D.M., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Developments in Mathematical, Statistical and Computational Sciences. AMMCS 2019. Springer Proceedings in Mathematics & Statistics, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-030-63591-6_15
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