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Abstract

A deep connection between intelligence and causal entropy maximization was sug- gested by Wissner-Gross and Freer in 2013 [1]: intelligence is moving towards a maximization of future possibilities. In this work I use the concept of causal en- tropic forces to investigate fundamental rules for pattern formation on a lattice. Previously, this has been studied in continuous space and time by Hornischer [2]. I explore three different approaches to calculate the phase-space volume, which is the crucial variable of the causal entropic force: approach A takes the raw number of possible trajectories into account and weights them equally. Here the force is strictly repulsive and the behavior is comparable to an ideal gas. Approach B takes the ra- dius of gyration as a weight for each sampling trajectory to explore the phase space volume. For this approach I find stable patterns, where the appearance ranges from hexagonal to labyrinthine depending on the time horizon and density. Approach C uses the boxcount of each trajectory as its weight. In this approach I find patterns, the appearance depending on time horizon and density but the occurrence also de- pending on the fraction of explored phase space. If only a small part of the phase space is explored the particles move erratically and no patterns appear.