Modulo 11 Fibonacci Pattern

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Contents

• The Unit cell.
• The Pattern.
• The Numbers.
• Art Gallery.

The Unit Cell

Whole pattern	Off Diagonal Elements

The Off Diagonal cells are generated by the sequences starting (3, 1), (3, 2) and (6, 2).

The Pattern

A number of unit cells are tiled to show the overall pattern.

The pattern composed from just the Off Diagonal cells.

The Numbers

The points are generated using an algorithm where the only input is the number of cells across the pattern. The resulting series for N=11 are shown below.

Seed	Sequence	No.
(0,0)	[0], [0], [0], [0],  ...	1
(1,1)	[1, 1, 2, 3, 5, 8, 2, 10, 1, 0], [1, 1, 2, 3, ...	10
(2,2)	[2, 2, 4, 6, 10, 5, 4, 9, 2, 0], [2, 2, 4, 6, ...	10
(3,3)	[3, 3, 6, 9, 4, 2, 6, 8, 3, 0], [3, 3, 6, 9, ...	10
(4,4)	[4, 4, 8, 1, 9, 10, 8, 7, 4, 0], [4, 4, 8, 1, ...	10
(5,5)	[5, 5, 10, 4, 3, 7, 10, 6, 5, 0], [5, 5, 10, 4, ...	10
(6,6)	[6, 6, 1, 7, 8, 4, 1, 5, 6, 0], [6, 6, 1, 7, ...	10
(7,7)	[7, 7, 3, 10, 2, 1, 3, 4, 7, 0], [7, 7, 3, 10, ...	10
(8,8)	[8, 8, 5, 2, 7, 9, 5, 3, 8, 0], [8, 8, 5, 2, ...	10
(9,9)	[9, 9, 7, 5, 1, 6, 7, 2, 9, 0], [9, 9, 7, 5, ...	10
(10,10)	[10, 10, 9, 8, 6, 3, 9, 1, 10, 0], [10, 10, 9, 8, ...	10
(3,1)	[3, 1, 4, 5, 9], [3, 1, 4, 5, 9], ...	5
(3,2)	[3, 2, 5, 7, 1, 8, 9, 6, 4, 10], [3, 2, 5, 7, ...	10
(6,2)	[6, 2, 8, 10, 7], [6, 2, 8, 10, 7], ...	5
Total		121

The Art Gallery

The following picture (and the background of this page) are examples of effects that can be obtained by taking the original rather sterile tiled picture and putting it through some effects in Paintshop Pro.