From Mathematics to Art: Petri Net Modelling of Tribonacciand k-Bonacci Petri Net Fractal Patterns

Simple recursive rules often conceal surprisingly complex structures, and the Tribonacci sequence is an interesting example of how elementary arithmetic can lead to complex and visually expressive patterns. In this research paper, we present triangular arrays generated by a Petri net encoding of the Tribonacci recurrence, extending our previous Fibonacci construction. Token propagation realizes the delayed dependencies of the recurrence and gives rise to a directed global triangular geometry. Parity and modular colourings highlight persistent self-similar motifs reminiscent of classical fractal patterns. We also outline higher-order k-bonacci extensions and compare the resulting visual structures. Within this framework, global fractal-like visibility tends to degrade as the order increases, while extreme orders can enter a different limiting regime.