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Wolfram Summer SchoolFounded in 2003

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


Narine Manukyan

Class of 2007


I am Narine Manukyan from Armenia. I study informatics and applied mathematics at Yerevan State University.

Project: 2,3 Mobile Automaton Behaviour

This project explores the step-by-step behavior of mobile automata with three colors. I ran these automatons through 1023490369077469249536 rules at about 315 steps each and applied filters to find complex behavior. One interesting result is that there are many cases where the initial behavior of the automaton is quite complex, but then it becomes repetitive after a certain number of steps with no recurrence of the complex behavior. In addition, I found some cases where the automaton's behavior was entirely complex with no repetitive behavior.

For example, one of my favorites is rule 513555777855555777. It starts with an initial condition {{1, 0, 2}, 0}, and the active cell is 1, 2, 3, or 5. In this example, there appears to be a triangular object that connects to the lower point of an adjacent triangle. At each iteration, the heights of the triangles increase. When we look at the overall behavior of this rule for a large number of steps, we can see how unpredictable it is.

Project-Related Demonstrations

3-Color Left/Right Mobile Automata

View demonstration of Wolfram Demonstrations Project

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 9011

I like CA 9011 because it creates a very interesting structure. If you consider white cells as forming paths to the top, and if there are moving points which start to move from the sides of that structure, those moving points never collide. So, in the output we will have a sequence of points emerging from the top of the structure.