At martian mid-to-high latitudes, the surfaces of potentially ice-rich features, including concentric crater fill, lobate debris aprons, and lineated valley fill, typically display a complex texture known as “brain terrain,” due to its resemblance to the complex patterns on brain surfaces. In order to determine the structure and developmental history of concentric crater fill and overlying latitude-dependent mantle (LDM) material, “brain terrain” and polygonally-patterned LDM surfaces are analyzed using HiRISE images from four craters in Utopia Planitia containing concentric crater fill. “Brain terrain” and mantle surface textures are classified based on morphological characteristics: (1) closed-cell “brain terrain,” (2) open-cell “brain terrain,” (3) high-center mantle polygons, and (4) low-center mantle polygons. A combined glacial and thermal-contraction cracking model is proposed for the formation and modification of the “brain terrain” texture of concentric crater fill. A similar model, related to thermal contraction cracking and differential sublimation of underlying ice, is proposed for the formation and development of polygonally patterned mantle material. Both models require atmospheric deposition of ice, likely during periods of high obliquity, but do not require wet active layer processes. Crater dating of “brain terrain” and mantled surfaces suggests a transition at martian mid-latitudes from peak “glacial” conditions occurring within the past ∼10–100 My to a quiescent period followed by a cold-desert “periglacial” period during the past ∼1–2 My.