Designing fractal activation functions for artificial neural networks

Activation functions play a central role in the expressiveness and learning capacity of Artificial Neural Networks (ANNs). While classical functions such as Rectified Linear Unit (ReLU) and Sigmoid have demonstrated practical effectiveness, they often lack structural complexity and adaptability. In this work, we introduce a novel class of fractal activation functions , derived from self-similar recursive structures inspired by fractal geometry. We develop a mathematical formulation based on Iterated Function Systems (IFS), integrate the proposed functions into feedforward neural networks, and evaluate their performance on the MNIST dataset. Our experiments reveal that fractal activation functions achieve faster convergence and higher test accuracy compared to conventional functions, while introducing only moderate computational overhead. These findings suggest that fractal-based activations offer a promising pathway to enhance neural architectures without modifying their overall topology. Accordingly, future work will explore optimization techniques, theoretical analysis, and applications to more complex learning tasks.