Power-Law Cascade to Model Growth of Teeth, Horns and Claws

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This Demonstration applies the power-law cascade model of growth to the shape of teeth, horns, claws and beaks of animals. A power law is used to model the dependence of the radial growth of the structure with its length to form a power cone. The power cone is twisted along a logarithmic spiral to form a power spiral. Click the buttons, for example, "tyrannosaurus rex", to simulate the tooth shape of different animals, or move the sliders to change the shape.


The sliders "spiral A", "spiral B" and " factor" affect the logarithmic spiral.

The sliders "power cascade C", "start angle", "range (radians)" and "radius" and the button "tip" affect the power cone growth.

The sliders "aspect ratio", "radial point", "transverse point" and "inner flat" modify the cross-sectional shape.

The slider "render points" and button "render quality" affect the speed and quality of the 3D mesh.

Click "export .ply file" to save the current shape as 3D ".ply" file.


Contributed by: Alistair Evans and Tim Wilson (May 2021)
(Monash University, Australia)
Open content licensed under CC BY-NC-SA




[1] A. R. Evans, T. I. Pollock, S. G. C. Cleuren, W. M. G. Parker, H. L. Richards, K. L. S. Garland, E. M. G. Fitzgerald, et al., "A Universal Power Law for Modelling the Growth and Form of Teeth, Claws, Horns, Thorns, Beaks, and Shells," BMC Biology, 19(58), 2021. bmcbiol.biomedcentral.com/articles/10.1186/s12915-021-00990-w.

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