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In 1999 there were two similar crop formations:

http://www.temporarytemples.co.uk/imagelibrary/images-1999-enlarge/39-Windmill-Hill-Wiltshire-16-07-99-Wheat-35mm.jpg

http://www.temporarytemples.co.uk/imagelibrary/images-1999-enlarge/58-West-Kennett-Longbarrow-Wiltshire-04-08-99-Wheat--35mm.jpg

The general pattern seemed like a fractal to me (though I'm no expert).
Using Adobe Illustrator I created a representation of this:


With the white square being the base unit 1, it is a 12x12 grid.
The center square is half of that (6).
Its "offspring" is half of that (3).
And then those squares have offspring which are a third of that (the base unit 1).
The smaller squares were added when I had the theory that it continues on from a third to a quarter,
but that is somewhat off-topic.

Using Fractal Science Kit, I made a L-system representation:

The white squares were added later for visual analysis.
I called the L-system b-order:
For those wondering what a-order is:
(These are some of my very first L-systems, so they could be overcomplicated.)

I later stumbled onto another way to create the pattern with FSK.
- General: Orbital / IFS / Strange Attractor
- Orbital Equation: Kotch Snowflake
- Properties: Number of polygon vertices: 4
(update: this pattern is actually half-half-half unlike the crop formations which are half-half-third
see post 14 to visualize)



Something very similar is produced with:
- General: Orbital / IFS / Strange Attractor
- Orbital Equation: Sierpinski N-gons
- Properties: Number of polygon vertices: 4
- Center point: checked

So does this pattern (fractal?) already have a name?
Thanks!

Hi kram,
Thanks a lot for pointing those out.
The T-square is definitely the L-system I was calling a-order (but did not include an image):


However, what I meant to show in the original post was that the two crop formations
follow the pattern of half-half-third, while the T-square is half-half-half. The Quadratic Koch seemed to also follow
the half-half-half pattern, although it was difficult to analyze with the method I have been using.
I guess I'll call the pattern in the original post: "b-order T-square", for now.

Interestingly, another crop formation appeared in 2005 that was the inverse of the two from 1999.
http://www.temporarytemples.co.uk/imagelibrary/images-2005-enlarge/20-East-Field,-Wiltshire-03-07-05-Wheat-OH.jpg

In other words: the pattern was 12-4-2-1, or third-half-half. An inverted b-order T-square... ;-]

That makes sense.

I wonder if there is any way to apply these patterns to computer architecture,
perhaps for heat dispersion. I believe fractals will be the foundation for future technology;
that and bio-mimicry (which I'm not sure can be separated from fractals).

This was interesting:

I appreciate the information!

Vicsek fractal
http://en.wikipedia.org/wiki/Vicsek_fractal






EDITED:
"Fractal Growth Phenomena" 2nd Edition
By (author): Tamás Vicsek (Eötvös Univ., Budapest)
Sounds as it is a name of author
http://www.worldscientific.com/worldscibooks/10.1142/1407

The fractal is named after Tamás Vicsek.

http://sins.xaoc.ru/pdf/articles/articles_e001.pdf
http://hal.elte.hu/~vicsek/publications/

Ryan

Thanks for the extra info guys.

I was thinking about the statement:


(regarding the T-square)

It seems that any T-square variation, or pattern inline with that statement,
could be used as a structure for efficient, high capacity, data storage.
I also see no reason why it would need to be limited to two dimensions.
Perhaps a T-square-cube of sorts.

I found, what I assume is, a more traditional approach to the T-square L-system here:
http://www.wolframalpha.com/input/?i=t-square+fractal

I plugged it into Fractal Science Kit, bent it in half and added a color pattern for fun.



I'll save all my Photoshop fun for deviantArt. ;-]

Thank you for furthering my point kram.

First idea:

Imagine a T-square lying flat on a table, and then extend it upwards (as though you are stacking many copies of it).
Then fill most of the space with inversions, or the Koch fractal (equal in height).
One could be used for the storage and the other for the flow of data.

Here's one possible top view, using the standard T-square:



I realized that my original claim that the Koch fractal followed the half-half-third pattern is erroneous.
It does in fact compliment the standard T-square.