Fibonacci Patterns

Original Fibonacci Patterns Page

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.)

The patterns on this page are mainly hand drawn and show some simple examples.

If you browser supports Googles's native client plug-in you can use the new interactive version. This will allow you to create more complicated examples, up to 600x600, and create animations by varying the size or starting parameters.

The examples on this page have (0,0) in the bottom left, the plug-in has (0,0) in the top left.

	Mod 2. Two colours, 4 squares.
	Mod 3. Two colours, 9 squares.
	Mod 4. 4 colours, 16 squares.

In the subsequent examples you can click on the images to see more information and some derivative patterns.

	Mod 5. Three colours, 25 squares.
	Mod 6. Four colours, 36 squares. This example also shows how patterns generated using composite numbers (6 = 2 × 3) include the patterns from their prime factors, in this case 2 and 3.
	Mod 7. Four colours, 49 squares.
	Mod 8. Eight colours, 64 squares. This also shows how this pattern relates to those of base 2 and 4 and also splits the pattern into "Diagonal" and "Off Diagonal" elements.
	Mod 10. Six colours, 100 squares. This really is a hand drawn pattern, the others are "hand drawn" on the PC. Click on the image for more information and examples. Also contains a discussion of the contribution of the prime factors to the overall pattern.
	Mod 11. Fourteen colours, 121 squares/
	Mod 12. 10 colours, 144 squares.

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