I've been working on some paintings that look like this:
(there's one that's not shown since it's mono chromatic and wouldn't really photograph well)
The paintings' composition is created simply by folding square pieces of paper. This is similar to a type of geometry known as flattened origami. Flattened origami is a fairly new branch of math that uses the creases from folding paper to solve complex calculus problems. I don't know calculus, but I know how to fold paper.
In fact, I'm sort of an expert of sorts. Just as one remembers long lost memories of a forgotten childhood with the slight whiff of a certain herb or spice (for me it's rosemary), the same can be said for tactile activities. Riding a bike after not being on one for years opens the floodgates to first memories of learning to ride a bike. It's muscle memory of a different type. Ever have a word you're trying to grasp? What do you do? You move your hands as if you're trying to feel it. If it's an object, you're trying to hold it. If it's an emotion, you're trying to act it out.
When I was younger, I folded paper constantly. You may have as well. Don't remember yet? Ever make a paper snowflake, or a paper airplane? Perhaps a "cootie catcher"? Or how about making a birthday card? And let's not forget Oriental origami. (little flapping birds).
Folded paper is everywhere. Napkins. Paper cups. Envelops. Cardboard Boxes. Magazines. Newspapers. Books.
Myself, I was the master of the paper airplane. I worked on creating the Best Paper Airplane in the World. My definition of the best was: performs awesome in all conditions. Light breeze, heavy winds, distance, tricks - the polymath paper airplane, like myself. A large task for a nine year old.
In the winter I was the maker of snowflakes. I remember accumulating plastic bags upon plastic bags of created snowflakes. Again, I always wanted to make the next snowflake better than the first.
And then there was origami. From the sparse collection of books from my grade school library to the next store neighbors Japanese friend who would come to visit, I had awesome training in this ancient art of paper folding. Going far past the flapping crane, I created camels, lions and jumping frogs. This sculpture isn't so much a subtractive process like carving or an additive process like clay, but a manipulative process that changed parts of the characteristics of the paper - basically by expressing a flat plane into multiple dimensions.
I guess for some reason, all these childhood insights and experiences came back to me. For all I know I was folding a piece of paper out of sheer boredom or monotony and thought that the creases looked neat. I then remembered a memory of watching a really cheesy show on TV (yes! childhood memories of TV!) called, Beyond 2000 which spotlighted technologies that seemed to come from, "The Beyond of 2000" (oohhhh). I don't remember the exact person they were interviewed, but it may have been Humiaki Huzita, who is a Japanese mathematician who came up with, Huzita's Axioms in 1992.
A brief aside. Calculus: invented around 1670. Recreational Origami paper folding in Japan: around 1600 (other forms, like certificate folding are even earlier). Huzuta's Origami Axioms: 12 years ago. 12 years!
So, I came sort of went round robin in this whole globalism thing where a Eastern solution is now being used to solve a Western problem.
I tried, really really hard to learn how to solve intense, mathematical problems using flattened origami. And I failed. I learned that flattened origami gets Real Hard, Real Fast. But how interesting such a simple device, a square piece of paper with creases creates such concepts out of the grasp of the average Joe (or in this case, me).
So, in a oft-used technique of mine although I did not invent it, I took a disadvantage; being completely awful at applied mathematics, to an advantage:
If I don't know the rules I can (1. make my own, (2. Discover things nonlinearly! - (going to step 123287918878 without first finished step 1)
So, hell yeah! This is what art is all about. This is why being an Artist is the coolest job in the world.
I got busy folding paper. I became really good at making neat designs and fell in love with the idea that anyone with a cheap piece of paper - the thinner/cheaper the better, can make designs just like mine, but it's almost never exactly the same, since pieces of cheap paper aren't grided (yes you can use grided paper you anal...fu - person) and paper folder is imperfect, since paper isn't really two dimensional, it has a thickness.
The more folds you make, the more complex the design appears to be. It's scoobies me to the point that I did not know how to create a model of the creases by writing a computer program - and what would be the point? Virtual paper - the beauty of paper is the tactility of it all!!
But, I came to some interesting conclusions.
If you fold a piece of paper over itself, as in, you don't unfold a crease you've made, when you do unfold all the creases, you'll notice that any point that intersects any line will create a symmetry:
The angles zooming out from the point are congruent. That holds for EVERY pair of lines that's zooming from every point! As complex as the web appears to be, there's this underlining order. Attempt to create this circumstance using a ruler and a pencil and you will fail.
Now, check out the colorization of my lines:
For these paintings, I basically took a big piece of paper, creased it and then transfer the composition to a canvas using the same technique you used for fresco painting. I then color coded the lines. The first crease is violet, followed by blue, green, red, orange and then finally yellow. Why only 6 creases? Because I only have six colors (the primaries and their complements), that can be readily distinguished from each other. Notice that the lines make shapes: three, four and five sided shapes. I haven't seen a shape more than six, but this may be tied to the number of folds (sides of the shapes made = # of creases - 1.. maybe)
Notice that no one shape has lines of the same color. So, I guess that would also mean that you cannot have a seven sided shape by folding a piece of paper six times.
The area of the shapes themselves are created by mixing the proportional amount of color from the sides. For example, if a shape makes a triangle that has sides with lengths 3, 4 and 5, with colors yellow, red and blue, I would mix a color that's 30% yellow, 40% red and 50% blue. This brings out the shape and helps you visualize the connection between it's neighbors.
You begin to see just how many different lines and types of symmetry there are in these suckers, from reflective, rotational, translational, to glide reflection -
Glide Reflection.
Glide Reflection is used a lot in Tessellations - which, if you don't know, are patterns that tile. Guess what? These paintings tile like nobody's business:
I think that's beautiful. It also reminds me of those coloring books that were just filled with patterns like these. Maybe your parents wouldn't allow you to color in the book itself, but you instead had to make photo copies of them.
Maybe this is how these patterns are created. I'm not really sure, but it's another neat throwback to childhood.
And here's my link from childhood to Now and how Art fits into all this. One of my favorite things to read up on is advanced Math and Physics - don't ask why, but that's how I got into all this flattened origami in the first place.
One of the problems with recent (as in the last 100 years) physics is that it introduces the idea of a world that has more than 3 directional dimensions. How do you visualize that?!
One successful way I've seen is within Dionys Burger's book, Sphereland, which gives the example of a fourth dimensional sphere passing through three dimensional space by suddenly appearing to a three dimensional being as a small sphere that gets ever larger and then smaller again.
Spehereland is somewhat based on Edwin A. Abbot's Flatland, which is all about two-dimensional creatures being visited by a three-dimensional being. The three dimensional being was a sphere and the way two-dimensional beings saw him was as a line that started as a point and got ever larger until it to disappeared. Think about the surface of a sink full of water being flatland and you dunking a ball into the water.
I see these paper foldings as showing multideminsionality. For example, take a square piece of paper and fold it. Unfold the piece of paper and examine the crease. A line is one dimensional.
Fold your piece of paper on the same crease as before and make another crease. Unfold the paper again see if the creases intersected, creating a point. You've now made something that's like a cartesian plane, with two lines, two one dimensional spaces, intersecting at a point. A cartesian plane is a two dimensional model.
You can continue to do this and I feel that the lines created are one dimensional realizations of multidimensional space. A flat line in the 6th dimension, the 6th crease that is, will create intricate shapes that curve around on each other, which end and begin at different places. Neat.
I know that this little idea is a bit flawed, but it's an interesting tool to grasp and imagine. And I also know that known of this is really ground breaking but it's a good example of my personal travels in playing with an idea, I guess that's what playing and Art are all about.
