the game of life
Here is an excellent article from Plus magazine that contains fun classroom activities and a nice applet for experimenting with the game of life. To see how a seemingly simple initial arrangement can give complex patterns, try starting with this 5 square arrangement shown!
A nice introduction to the game of life may be to do this maze puzzle from the excellent clickmazes. There are other game of life related puzzles at the bottom of that page, such as the Y-start challenge.
If you do not have enough computers, you could generate patterns using counters, or it could be more fun to do it with real people!
My year 12 students experimented with the applet and posted some of their results on our maths-based facebook page Delicious Pi. One of the students investigated the results of starting with different rectangles and found some interesting patterns. Perhaps this could be developed into an interesting investigation?
There are various other questions posed in the above article that should generate other interesting investigations. Or you could try changing some of the rules slightly, or even try inventing a similar game of your own?
Finally, I found this interesting coral image (below) in the excellent Games and Puzzles Journal which is available to download for free and contains loads of interesting ideas that could be used in the classroom.
A nice introduction to the game of life may be to do this maze puzzle from the excellent clickmazes. There are other game of life related puzzles at the bottom of that page, such as the Y-start challenge.
If you do not have enough computers, you could generate patterns using counters, or it could be more fun to do it with real people!
My year 12 students experimented with the applet and posted some of their results on our maths-based facebook page Delicious Pi. One of the students investigated the results of starting with different rectangles and found some interesting patterns. Perhaps this could be developed into an interesting investigation?
There are various other questions posed in the above article that should generate other interesting investigations. Or you could try changing some of the rules slightly, or even try inventing a similar game of your own?
Finally, I found this interesting coral image (below) in the excellent Games and Puzzles Journal which is available to download for free and contains loads of interesting ideas that could be used in the classroom.
maths in nature
This idea of simple mathematical rules generating seemingly chaotic behaviour is something Alan Turing investigated in the later part of this life; this excerpt from the BBC4 documentary 'The Secret Life of Chaos' explains this idea:
Morphogenesis concerns the development of cells and describes how they self-organise to create patterns. In recent years many biologists are starting to see the implications of Turing’s work on morphogenesis, from animal skin patterns to the way bacteria develop. Here are some photographs:
These images and the idea that simple mathematical rules govern complex behaviour in nature brings to mind fractals.
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