The branching patterns of radiating ridges on surfaces of tensile joints and shatter cones were simulated and quantified, and their scaling properties were examined in three dimensions by means of a technique new to geology, the slit-island method. Results show that the textures are fractal over a wide range of scales. Accordingly, an algorithm simulates growth of tensile fracture-surface features by combining a set of rules with an element of randomness. The simulated surfaces are fractal and strikingly similar to natural fracture surfaces. These and other complex branching patterns observed in geology are likely due to an interplay of deterministic and random processes.

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