Wolfram Computation Meets Knowledge

Wolfram Summer School


Leo McElroy

Science and Technology

Class of 2017


Leo is a physics/computer science major at Middlebury College in Middlebury, Vermont. He is currently developing his understanding of complex systems with the hope of ultimately applying this understanding to the design and engineering of such systems. He is in the process of cofounding his school’s Makerspace. His own making has involved digital fabrication, embedded systems, computer-generated art and bioinformatics projects. Leo also has an interest in learning theory and educational reform. In addition to his intellectual pursuits, he enjoys travel, hiking, climbing, eating mystery foods and adventure in general.

Computational Essay

Sandpile Model for Self-Organized Criticality »

Project: Predicting Macro-Effects of Rule Variations in the Sandpile Model

Goal of the project:

To investigate the behavior of simple programs inspired by the Bak–Tang–Wiesenfeld sandpile model, and to explain specific characteristics of sandpiles from underlying rule matrices.

Summary of work:

I investigated all 255 Moore neighborhood rules, with critical heights from one to eight and each grain of sand being uniquely distributed. All rules were sand conserving. I looked at models with randomly added sand and with sand added only to the center cell. The focus of my investigation was sandpiles on a 301 x 301 table with 3,000 grains of sand.

Results and future work:

  • Qualitative: I frequently observed a transient chaotic phase that stabilized to a periodic limit cycle.
  • Quantitative: I was able to accurately predict the growth direction of unidirectional sandpiles. I also attempted to derive growth rate from underlying rule matrices and determined a coarse measure.
  • Future Work: Future work could entail devising a more accurate measure of sandpile growth rate, investigating randomly seeded piles and describing other features of sandpiles in terms of rule matrices.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022