JW's Fibonacci Patterns Module

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xS

Displays a range of patterns of different sizes using the default seed map value of 1, which selects just a single seed. The image is scalled to fit the window as close as possible.

xT

Displays the same range of patterns as 'xS', but this time the patterns are tilled to fill the available space using a fixed cell size.

xT m13

This is similar to the previous pattern, but now 'm13' sets the seed map to 13, selecting the first, third and fourth seeds (1 + 4 + 8).

xT tA r23 n3 i100

This pattern uses 'tA' (advance seeds mode) to step through the 11 non-zero seeds of the 23×23 pattern (r23) in bunches of 3 (n3). The seeds follow the sequence (1,2,3), ..., (1,2,11), (1,3,4), ..., (9,10,11) and then back to (1,2,3). The 'i100' parameter tells the application try try to draw 10 patterns per second (100 milliseconds), reality might be slower, depending on your computer. The sequence has 165 members so the patterns will repeat every 17 seconds. The 'r24' pattern has 30 seeds and the cycle would take about 6 minutes. If you were to combine 'r24' with 'n14' you would produce a cycle of 29!/(14!×15!) patterns, taking about 3 months. 'r29' will give you 62 non zero seeds, which with 'n3' would cycle in just over an hour. However combine 'r29' with 'n31' and you'd have a sequence that repeats about once every 1.4 billion years.

xT tA r23 n3 i100 c2

The same pattern as before but with smaller cells (2×2) giving more copies of the pattern

tV r49 c11 1000

'tV' selects the vary seeds mode, stepping through the combinations of seeds sequencially. The seed map is a set of 32 flags, corresponding to the first 32 seeds. The 49×49 pattern has 24 non-zero seeds so the cycle will contain 16777216 patterns, siz months at one per second.

tC c1 i100 xT r2-200

'tC' selects complete mode which colours in all the cells. The colours are reused when there are more seeds than colours.

tS r597

Shows the seeds for the r597 (597×597) pattern, which has a noticeable fractal pattern.