The visual complexity of orthographies varies across writing systems. Prior research has shown that complexity strongly influences the initial stage of reading development: the perceptual learning of grapheme forms. This study presents a computational simulation that examines the degree to which visual complexity leads to grapheme learning difficulty. We trained each of 131 identical neural networks to learn the structure of a different orthography and demonstrated a strong, positive association between network learning difficulty and multiple dimensions of grapheme complexity. We also tested the model's performance against grapheme complexity effects on behavioral same/different judgments. Although the model was broadly consistent with human performance in how processing difficulty depended on the complexity of the tested orthography, as well as its relationship to viewers' first-language orthography, discrepancies provided insight into important limitations of the model. We discuss how visual complexity can be a factor leading to reading difficulty across writing systems.