The Abstraction and Reasoning Corpus (ARC) has emerged as a key benchmark for evaluating progress toward Artificial General Intelligence (AGI), as it emphasizes flexible problem solving and generalization beyond narrow, domain-specific methods. This thesis investigates the application of Genetic Programming (GP) to the ARC framework, with the aim of exploring the feasibility of evolutionary search as a path toward generalizable reasoning systems. In this work, we describe our attempt to use the Byron fuzzer (Byron: A Fuzzer for Turing-complete Test Programs, 2024) to tackle ARC tasks, focusing on fitness evaluation, transformation functions and program structure. We analyze the performance of the system on different ARC challenges, highlighting its potential and limitations.