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We study the dynamics of a thin film over a substrate heated from below in aframework of a strongly nonlinear one-dimensional Cahn-Hillard equation. Theevolution leads to a fractalization into smaller and smaller scales. Wedemonstrate that a primitive element in the appearing hierarchical structure isa dissipative compacton. Both direct simulations and the analysis of aself-similar solution show that the compactons appear at superexponentiallydecreasing scales, what means vanishing dimension of the fractal.

Superexponential droplet fractalization as a hierarchical formation of dissipative compactons