Lindenmayer systems and primes

TL;DR

This paper investigates the distribution of primes associated with letters in an infinite word generated by a simple Lindenmayer system, proposing a conjecture about the growth rate of their discrepancy tending to e.

Contribution

It introduces a conjecture relating the discrepancy growth rate of primes in Lindenmayer system words to the mathematical constant e.

Findings

Discrepancy between prime counts for two letters analyzed

Conjecture formulated on discrepancy growth rate tending to e

Empirical evidence supporting the conjecture

Abstract

We study the surprising discrepancy between the number of primes corresponding, respectively, to the two letters of an infinite word engendered by one of the simplest Lindenmayer systems. We formulate a conjecture concerning the rate of growth of this discrepancy, which seems to tend to e for every two sufficiently high consecutive even rank iterates of the Lindenmayer system.