Turing machine simulations

Why study so many examples? –Get an intuition for what goes on inside computers without learning all the details of a programming language –Complex tasks performed by sequence of very simple instructions Emergent complexity –Very simple rules lead to very complex behavior –Scientists try to understand how our universe can be so complex when physics is simple

Multiplication and sample output Addition and doubling programs Recognizing a language A sorting Turing machine Addition and subtraction Addition, divisibility, and primality Turing Kara Wolfram’s Version of Turing machines –Explain notation –Explain 3-state 2-color TM

Minsky’s small universal Turing machine –Explain transition function notation Two-dimensional TM from Wolfram –Binary counting Turmite (90 degrees left) –Initially arrow faces up –Little square, original color. –Big square, new color. –Other patterns produced by various turmites A random pattern produced by a Turmite –Binary counter, started with two black squares

Langton’s Ant –Believed to start a highway from any intial pattern Turmite simulations –Click on “Launch Turmites” –Click on “Load” –Choose turmite –Click on “Load” –Click on “Fast” then “Zoom out” –Can edit rules too

John Conway’s Game of Life –Show rules –Do a few random patterns, see what happens Turing Machines in Conway’s Game of LifeTuring Machines in Conway’s Game of Life Patterns, Programs, and Links for Conway's Game of LifePatterns, Programs, and Links for Conway's Game of Life –Click on a picture to run the game of life –Do a few selected topics