"Non Repeating" Area Fill Patterns

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"Non Repeating" Area Fill Patterns

Post by Matt_A » Tue Oct 01, 2019 1:35 pm

In North America there is a species of cicada that has two branches, which reproduce on slightly different life-cycles - one hatches every 17 years and the other every 13 years. Because these numbers are prime to each other, members of each brood only interact once every (13*17) 221 years.

You can use this principle to construct simple tiling patterns that do not appear to have a repeat pattern to the human eye. So if you want to, for example, put a texture on a lawn area, without it presenting evidence and the distraction of a repeat pattern, here's one way that does not involve a coded procedure. This method uses three component source patterns (although two would generally give reasonable results).

They are 13"x13", 17"x17", and 23"x23". The ultimate pattern generated has a repeat of 13*17*23 = 5083" or 423'-7" . This should be good enough for most purposes :roll:
p1.JPG (11.15 KiB) Viewed 4299 times
first repeat each one on it's own module (top row is 13" elements at 13" spacing, next 17" at 17" spacing, bottom is 23" at 23" spacing). Your eye has no difficulty perceiving the repeated elements.
p2.JPG (33.13 KiB) Viewed 4299 times
When these resulting rows are then each repeated vertically (i.e. at 13", 17", and 23" spacings respectively) the pattern is even, and your eye detects that it is made of consistent elements, but there is no apparent "grid" to the fill.
P3.JPG (111.65 KiB) Viewed 4299 times
If I were planning to use this pattern in a drawing I would probably make some adjustments to eliminate the 'rivers', it would not take much. This technique gives an even, predictable tone.

Here is the same pattern except without the 13" element, just the 17" and 23" ones. This pattern repeats every 23'-0", but your eye can detect the constituent elements with a little effort.
p4.JPG (92.96 KiB) Viewed 4299 times
And this is an image of the same objects with different attributes: Lineweight scaled up by 50x, opacity set to 20%, end caps to NIL, and the two patterns in slightly different greens.
p6.JPG (85.55 KiB) Viewed 4299 times
You can tell that there are repeating elements, but you can't really see where they repeat from...

Like the cicadas, the essential feature is that the sizes of the elements and their repeat distances be the ratio of numbers that are prime to each other.

here's the same pattern as the green one above, except these lines are all the same color, the lineweights are half as wide and End Caps are set to round:
p7.JPG (72.74 KiB) Viewed 4287 times

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