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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA

Alumni

Wiktor Macura

Class of 2004

Bio

Wiktor Macura was born in Poland in March 1990. He is currently a junior at the University of Maryland, Baltimore County, majoring in Mathematics and Computer Science. Beside his interest in computer graphics and artifical intelligence, he also plays the flute and has a black belt in Tae Kwon Do.

Project: Extended Turing Machines

A typical Turing machine consists of a "head" and a "tape." For every instruction the head may be either in the read or write position (up and down, respectively) and the head may either move left or right by one step on the tape. Furthermore, the tape may only be written at the head. I intend to study Turing machines where a particular slot on the tape can only be in two states (in other words, two-color Turing machines). However, for all of the 4096 programs, none of them produce interesting behavior.

I intend to look into so-called n-jump Turing machines (temporary name) where the head may move at most n steps in either direction per step in the execution. The expected result is that a 2-jump Turing machine will start to show interesting behavior. However, if this is not the case then I will study successively larger jumps to see where interesting behavior begins. Of particular interest is attempting to explain why the behavior becomes complex with a particular jump size.

Favorite Two-Color, Radius-2 Rule

Rule chosen: 195657

The most interesting two-color, range-2 Cellular Automaton I found was rule 195657. The behavior appears to be generally random; however, the left edge of the triangle is what makes this rule interesting (this is for a base step of a single black cell). Also, for a base step of {1, 1} the automaton starts acting really funny.

It is interesting to note that a base step of {1, 1, 1} continues producing interesting behavior while a base case of {1, 0, 1} does not (a nested pattern). This is interesting because if we look at the second step we see that it is in fact {1, 0, 1}; however, there is a long line on the right. This seems to suggest that these lines are important to the behavior of the rule.