These patterns are generated by generating Fibonacci sequences in modulo arithmetic and the plotting consecutive pairs of values as co-ordinates. See the Algorithm page for more details.
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Mod 2. Two colours, 4 squares. |
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Mod 3. Two colours, 9 squares. |
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Mod 4. 4 colours, 16 squares. |
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Mod 5. Three colours, 25 squares. |
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Mod 6. Four colours, 36 squares.
This example also shows how composite numbers include the patterns from their prime factors, in this case 2 and 3. |
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Mod 7. Four colours, 49 squares. |
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Mod 8. Eight colours, 64 squares. Shows how this pattern relates to those of base 2 and 4 and also splits the pattern into "Diagonal" and "Off Diagonal" elements. |
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Mod 10. Six colours, 100 squares. This really is a hand drawn pattern, the others are "hand drawn" on the PC. Also contains a discussion of the contribution of the prime factors to the overall pattern. |
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Mod 11. Fourteen colours, 121 squares |
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Mod 12. XXX colours, 144 squares |