Waking Up To the Higher Level

Earlier, when we overlapped circles new shapes emerged that we did not directly create: flowers. 
If we overlap hexagons in precise columns and rows our mind will see all kinds of shapes rise up:
and the cubes can line up this way, or that way…
Can you catch yourself flipping between these perceptions– boxes this way and boxes that way?
When you catch your mind perceiving in different ways you are watching your own thinking. In other words, you are doing metacognition: thinking about your own thinking.  How many things in the universe can do that? How many things can recognize their own thoughts and ask: is there a better way for me to do this?
Computers can. 
And that is very powerful. 
Our sense of self in part derives from recognizing our own thoughts. 
For the first time in history machines are starting to do the same: to think about their own thinking. Learning algorithms use metacognition to improve how they learn. These are algorithms that improve themselves based on experience. 
In making your math and art statements you guys are playing with the same sort of concepts. Not only do your creations encourage people to think about their own thinking, but to some degree the programs you write also use metacognition: One process in your program watches the other to know when to stop the madness and break out of the infinite loop. For example, the
If machines can improve their own thinking, and if thinking about your own thinking leads to consciousness (recognizing self) then do you think machines will become self aware like us?
You have already started creating a process which I think is a building block towards this sort of artificial intelligence and self awareness. 
You created a program that refers to itself (recursion). It takes the output of what it did (stamp a square) and transforms, takes the output of that and transforms it, takes the output of that and transforms it… and so on. 
There’s a famous artist who, inspired by Islamic designs, created art that plays with these sorts of concepts: recursion, self-reference, self awareness– just as you are doing. Let’s look at his work to help you go further with your own art and creative math…
(bird flying off to link to his stuff)