One day, during a meeting, I sketched some pictures into a graph paper engineering notebook. A few days later, I expanded the pattern on another page and filled it in with highlighter. It looked really cool! There was an actual thought going through my head as I made it: I wanted to see how just a few simple operations could build up a complex figure.
Each picture is described with a number that describes the operations necessary to create it. Each picture begins with a 2x2 grid, which gets copied 3 times to form a 4x4 grid. Every iteration doubles the width and height. As the previous generation is copied, it gets rotate either 0, 90, 180 or 270 degrees. Optionally, it can be mirror-flipped, too.
I had mostly forgotten about it until a few months ago when I moved and found the original blue and green picture on light yellow paper with dark green quad ruling. After hanging up the torn-out page on my apartment wall, and re-considering it, I decided many more similar patterns can be produced. So, I coded up a version of the algorithm in perl, and now I've got hundreds of pictures from it!
Since there are so many different pictures, I can't possibly talk about all of them, but I'd like to comment on a few of them and leave you with a link to a directory that has many more for you to explore. And remember, when fashionable ladies are wearing this on their skirts in a few decades, you saw the patterns here first!!
Here it is...the first pattern I drew in my notebook so many years ago:
Now, let's examine some variations. This one is some kind of maze-thing.
This is an awesome-looking maze-thing. Notice how the white background connects all parts of the picture
Yup, some patterns come out nice and boring!
I LOVE this one! it's got these big, funky-looking 70's type blocks to it!
Alright, this one is a variation of my original pattern, with a high degree of symmetry. Notice, too, how most of it is all connected.
oh my! changing a few parameters has turned it into a field of flowers!
Yet another version of my original pattern. Exhibits a different type of symmetry, again, connected.
This variation on the original is awesome...or maybe it's just the inverse???
I love this variation! It has expanded versions of the "King Tut" and "deformed Ninja star" patterns that I liked so much on the original graphic.
Ah, yes! The Berzerk maze of Ninja stars!
And who could forget the Mah Johng Table!
Here! One of my all-time favorites! To me, it looks like little fetuses inside wombs! See how some are twins! There are also quadruplets, and single babies. Notice too, the lack of periodicity, resembling a Penrose tiling.
You gotta love this one, just because it's so...ummm...Square!