Mapping life's disparity and evolutionary constraints in a geometric complexity space

The Earth's biosphere exhibits a notable diversity of forms, yet the full morphological extent and limits of life remain largely unexplored. Here, we develop a geometric complexity space for comparing all known unicellular and multicellular phyla using fractal descriptors of the density and heterogeneity of body mass and structure. By applying this approach to a large set of extant biological shapes, we show that life exploits a tiny portion of structural possibilities, clustering around linear, rounded, and densely structured forms, while consistently avoiding complex heteromorphic ones. We show that this restriction results from deep physical, metabolic, and developmental limitations, shaped over geological time by the evolution of body size and ecological lifestyle. Our findings provide a global, quantitative perspective on the long-standing interplay between chance and necessity in evolution, with implications for the expected forms of life beyond Earth.