1. Turing machine simulations

2. 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

3. 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

4. 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

5. 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

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