Component for melting or distorting a structure.

Hi , so been trying my hand at ways to distort this definition (download) and the definicion consists on a series of tessellations that follow a set of curves, but I would like to know if i can somehow distort the first few tessellations at the base, so instead of having hard shapes you would end up with a sort of foam or melted structure that progressively changed its shape until you end up witht he original tessellation ont he upper levels.

Its so that they don´t look exactly the same but also i want to distort them enough so that people can know they are related, like they still held a conection but with a difference, like they got exposed to ehat or something neat the base.

Thank you, hope someone can help, thanks.