  We study the dynamics of a thin film over a substrate heated from below in a
framework of a strongly nonlinear one-dimensional Cahn-Hillard equation. The
evolution leads to a fractalization into smaller and smaller scales. We
demonstrate that a primitive element in the appearing hierarchical structure is
a dissipative compacton. Both direct simulations and the analysis of a
self-similar solution show that the compactons appear at superexponentially
decreasing scales, what means vanishing dimension of the fractal.
