On Mars, near the equator, much of the terrain in Gale Crater consists of bedrock outcrops separated by relatively smooth, uniform regolith surfaces. In scattered sites, however, distinct patterns—in the form and texture of the ground surface—contrast sharply with the typical terrain and with eolian bedforms. This paper focuses on these diverse, intriguing ground patterns. They include ∼1 to >10 m‐long linear disruptions of uniform regolith surfaces, alignments, and other arrangements of similar‐sized rock fragments and shallow, ∼0.1 m‐wide sandy troughs 1–10 m in length. Similar features were recognized early in the Mars Science Laboratory (MSL) mission, but they received only limited attention until Curiosity, the MSL rover, encountered striking examples in the Glen Torridon region. Herein, the ground patterns are illustrated with rover images. Potential mechanisms are briefly discussed in the context of the bedrock composition and atmospheric conditions documented by Curiosity. The evidence suggests that the patterns are active forms of spontaneous granular organization. It leads to the hypothesis that the patterns arise and develop from miniscule, inferred cyclic expansion and contraction of the bedrock and regolith, likely driven by oscillating transfers of energy and moisture between the atmosphere and the terrain. The hypothesis has significant implications for studies of contemporary processes on Mars on both sides of the atmosphere‐lithosphere interface. The ground patterns, as well as ripples and dunes formed by the wind, constitute remarkable extra‐terrestrial examples of granular self‐organization, complex phenomena well known in diverse systems on Earth.