Abstract More precise measurements of the complexity of leaf shapes can open new pathways to understanding plant adaptation and resilience in the face of global changes. We present a method to measure the complexity of plant leaf shapes by relating their fractal dimension to topological entropy. Our method relies on ‘segmental fractal complexity’ and stems from a fractal-thermodynamic system analogy. The complexity of plant leaf shapes is an algebraic combination of the fractal dimension of the components, leaf lamina, background, and leaf edge. We applied this method to leaf forms of 42 tropical plant species. Segmental fractal complexity is an improvement over the leaf dissection index because of its ability to capture the spatial positioning of a leaf’s lamina, edge, and background. It is also an advancement over conventional geometric and fractal dimension-based measures of leaf complexity because it does not entail information loss due to the pre-processing and is perceptibly simple.