Modulo 6 Fibonacci Pattern


Contents

The Unit Cell

The 6 x 6 pattern incorporates those from 2 x 2 and 3 x 3 as shown in the illustration.

N = 6 N = 2 N = 3

The Pattern

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

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=6 are shown below.

Seed Sequence No.
(0,0) [0], [0], [0], [0], ... 1
(1,1) [1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 0, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 0], [1, 1, 2, 3, ... 24
(2,2) [2, 2, 4, 0, 4, 4, 2, 0], [2, 2, 4, 0, ...

= 2 * [1, 1, 2, 0, 2, 2, 1, 0], ..., the corresponding series in the order 3 pattern.

8
(3,3) [3, 3, 0], [3, 3, 0], [3, ...

= 3 * [1, 1, 0], the corresponding series in the order 2 pattern.

3
Total 36