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Turing machine simulations

Delve into Turing machine simulations to gain insight into computer operations, complex tasks, emergent behavior, and the simplicity behind complex universes. Discover examples like multiplication, addition, sorting, and more to grasp essential concepts. Explore Langton's Ant, Turmite simulations, and Conway's Game of Life for hands-on learning.

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Turing machine simulations

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  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

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