Since the number of networked devices increases continuously, ensuring the safety and reliability of these systems is growing at the same time. Today, a unique identity of a device can be obtained from physical unclonable functions (PUFs) and this identity as a trust anchor in higher-level security architectures. This article is exploring the cellular automaton (CA) paradigm to extract and magnify unique features of the underlying hardware to uniquely identify a device. The proposed PUF is based on a field-programmable gate arrays (FPGAs) implementation of CA with random memory (CARM) model. Implementation of the memory part of CARM is the challenge of the introduced PUF, and corresponding response is obtained from the introduced evolution figure metric. The uniqueness and reliability of the PUF hardware are compared with the results from the state-of-the-art PUF designs implemented on FPGA in the literature. The test results show that the introduced CA-based design is a promising and competitive candidate for PUF primitives.