Wolfram Computation Meets Knowledge

Wolfram Summer School


Vallorie Peridier

Summer School

Class of 2008


Vallorie Peridier is both associate professor and graduate-program director in the mechanical engineering department of Temple University, located in Philadelphia, Pennsylvania.

She earned her physics undergraduate degree at Bryn Mawr College, and her applied-mathematics doctoral degree at Lehigh University.

She has found her participation in the NKS community to be a transformative experience, and her goal is to abet the recognition and adoption of NKS methods in engineering applications.

Project: CA-Generated Idealizations of Roughened Surfaces

Models of surface roughness, utilized in numerical simulations, often entail an ad-hoc randomizing strategy. Such approaches frequently result in a less than satisfactory approximation of the surface topology.

This study demonstrates how a basic cellular-automaton (CA) approach can be used to construct a somewhat more plausible representation of a roughened surface.

The basic idea entails interpreting the cell-by-cell accumulations of totalistic 2-color CA evolutions as the vertical offsets for nodes that define a triangulated, faceted surface. This approach provides an interesting variety of irregular but physical-appearing surface structures.

In summary, this CA rough-surface model successfully articulates a quite complex surface geometry with only a very modest-sized rectangular data grid which, with suitable interpolation functions, could be subsequently exported to other computational applications.

Project-Related Demonstrations

Reversible Two-Color Cellular Automaton Rules

View demonstration of Wolfram Demonstrations Project

Favorite Radius 3/2 Rule

Rule invert rule

A rule is reversible if there is an “invert rule” that exactly runs the rule “in reverse” for any initial condition. I found 16 reversible rules in the k=2, r=3/2 rule space, and identified invert rules for all 16.