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Wolfram Summer SchoolFounded in 2003

16th Annual Wolfram Summer School, held at Bentley University June 24–July 13, 2018


Carl Wahl

Class of 2014


Carl was born and raised in Madison, Wisconsin, and is currently finishing his bachelor's in physics at the local university. Many topics in science and technology fascinate him. He sees things that would better the lives of people all over the world as particularly important. These may include autonomous vehicles, carbon-free energy production, advanced imaging techniques, and medicine. It is wonderful to imagine the benefits if these problems could be solved. At the moment, he works in a plasma physics laboratory that studies the action of dynamos and other astrophysical phenomena. This has given him an excellent introduction to laboratory techniques and the scientific process. He is working to better understand how plasma behaves. One day he hopes to aid in the design, construction, and operation of nuclear fusion reactors for worldwide energy production.

Some of his hobbies include golf, skiing, electronics fiddling, fishing, juggling, and disc golf.


Plasma, sometimes referred to as the "fourth state of matter", consists of gaseous, charged particles. When a gas is sufficiently heated, bound electrons may gain enough energy to escape their positive nuclei. We then get a sort of "sea" of unbound, negatively charged electrons and positive ions. As electrons continually escape and recombine with positive ions, energy is emitted in the form of light. Oftentimes this light is in the visible spectrum, and we are therefore able to see the plasma itself. Common examples of plasmas include our sun, the gas inside fluorescent lights, the aurora borealis (northern lights), neon signs, and the gas inside of an experimental fusion reactor. Things such as jumping sparks generated after rubbing your feet on the carpet, lightning, and cathode ray tubes (CRTs) might also be called "discharge plasmas". Plasmas come in all sorts of colors and "flavors". They can form from any mixture of gas, homogeneous or not, as long as enough energy is supplied.

My project will investigate the behavior of gaseous plasmas using cellular methods of programming. The approach of traditional physics has been to construct systems of equations in order to solve for the evolution of plasmas. However, in order to be able to write succinct equations on paper, some approximations become necessary. This, unfortunately, means that information on certain effects may be lost, and plasma observed in the real world will not agree with what was predicted. My ultimate goal is to avoid such oversights so that a more accurate model can be achieved. This could lead to much greater understanding, and the development of useful technologies such as viable sources, of fusion energy.

The Ginzburg-Landau equations contain a model which can be used to describe complex spatiotemporal patterns. Plasmas are full of waves, so this model may be useful in describing its behavior. I plan to study this model and search for an efficient way to implement it using cellular automata. I will also search for ways in which the simulations of discrete plasma particles may be made more efficient, possibly by taking advantage of symmetries. The behavior of plasmas are based on simple physical laws, such as the Lorentz force law of electromagnetism and Newton's laws of motion. It follows that simple rules governing cell transformations could be used to simulate plasmas.

Favorite Outer Totalistic r=1, k=2 2D Cellular Automaton

Rule 231908