Langton's Ant

Homeschool Science Lesson Idea

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A fun and interesting thing to look at in your homeschool science lesson is Langton's model of an Ants Universe.

Since the late 19th century scientists have been looking for a Grand Unification Theory (GUT) - a theory that will cover life, the universe and everything. But what will we know if we find it? This simple model tells us something of the consequences.

Here is how to explore it in your homeschool science lesson.

Homeschool Science

Langton's Ant was invented by Chris Langton in 1986. It is a very simple model of an ant in a universe (or grid). The ant knows all the rules of its universe, because they are so simple ;

  • Rule One : if the ant is on a white square is must turn left and move one square forward. The square it moves out of turns black.
  • Rule Two : if the ant is on a black square, it must turn right and move one square forward. The black square it moves from will turn white.
  • Langton's ant

    This is quite a simple model to set up with your children on graph paper and either some squares of black and white (or colored) paper - or some Orthello counters. Begin in the center of the grid and begin to move the ant according to the rules of its universe.

    At first we think we can predict what will happen because the rules are so simple - but as the ant keeps moving, the pattern it creates becomes more complex. After a few hundred steps the pattern begins to break down and chaos develops (much like chaos theory of our universe).

    If we program the ants movement in a computer program, we can see that at 104 steps, the ant begins a very specific road-like patterning (known as a highway). The ant has displayed 'emergent behaviour'. This is a branch of mathematics that is used for lots of things (such as forecasting the weather).

    You can download a program to do this from here or or try it online.

    If we add more complex rules into the universe - such as using more than two colors or setting up obstacles, then we see even more complex behaviour. Scientists think that Langtons Ant will always produce 'highway' behaviour at some point - but they cannot prove it.

    You can see some wonderful examples in this video.

    Even though scientists understand the rules behind the ants universe - they cannot predict analytically exactly where the ant will be after a certain number of moves.

    So even if we eventually learn all the rules about our universe with the General Unification Theory, we will still not know everything about it, or be able to predict outcomes. We will still have a lot to learn!

    Find out more :

  • Lesson Plan

  • Wikipedia

  • Chaos Theory Mathematics for Kids


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    More Homeschool Science?
    Why not take a look at the periodic table for kids.

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