Turing machine simulations Why study so many examples

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 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