Symmetry
Symmetry might be thought of as a change that makes no difference.
Imagine an infinite floor tiled in a checkerboard pattern. If you change position by walking across the floor what you see doesn't change.
Or as https://www.chessprogramming.org/Chessboard puts it: "The four axis are the vertical line between the two center-files 'D' and 'E', the horizontal line between the 4th and 5th rank, and the main-diagonal and main-anti-diagonal. The orthogonal symmetrical squares have different, the diagonal symmetrical squares have the same square-colors."
Symmetry is important in physics. The conservation laws of physics are caused (I've read) by various sorts of symmetry. Of course symmetry is at the center of crystallography.
Evolution uses symmetry in many ways. We have a bilateral symmetry that we share with many other creatures. The genetic instructions for creating my left arm are the same as for my right arm but with a mirror symmetry. I think that various symmetries are visible in an embryo long before it has things like arms.
Creatures with eyes that move around in reality are very sensitive to visual symmetry. Symmetry picks out other animals as different in kind from rocks and trees and flowers. It's a capability that increases survival rates and therefore is selected by evolution whenever it occurs.
Other creatures who don't need to move around like we do have adopted other symmetries as the basis for their body plan. Radial symmetry is common among creatures who live fixed to a spot whose food can come from any direction.
The human perceptual system is very sensitive to visual symmetry. Visual symmetry attracts our attention. But also, like a chessboard, symmetry can be visually boring. Wallpaper presents a strong visual pattern that is designed to bore our attention and fade out of our awareness.
With a few exceptions, like the great MC Escher, most artists seem to dislike symmetry. Asymmetry is considered to be more 'interesting'. When I was a photographer I learned to use the 'rule of thirds' as a compositional tool and that was a tool designed to break symmetries.
I've always liked playing with symmetry tho. As a photographer I could easily play with mirror symmetry by just flipping the negative over and I liked how that manipulation added an extra element to the picture.
About 15 years ago I started working with a kind of symmetrical picture I call a snowflake. I started with the hexagonal symmetry that real snowflakes show, I found that the radial symmetry caused the elements of the image to merge into new shapes and relationships. Besides a six sided polygonal snowflakes you can do 5, 8, 9, 10, 12 sided radial symmetries.
https://www.simulat.ca/compositions2.php?filename=dots-qop.jpg
I've made thousands of these pictures now and I've learned a lot. At first I was just exploring the amazing possibilities the method offers. Over time I've gained more control over the image. The method starts with a seed image and successively selects triangular regions to recombine with a radial symmetry. I can look at a seed and get a pretty clear idea of what sort of picture it will make.
This winter I've been taking pictures of the scene framed by the grove of trees outside my window and making a new picture every day or so. So far I have about 60 very different pictures of the same scene. The seeds vary according to the light outside and on the trees and then each goes through a snowflake transformation.
Lately I've been working with hexagonal snowflakes. Hexagons can tile a plane and the resulting tesselation adds a new level of interest or turns the image into wallpaper that fades from awareness.
I enjoy making snowflake images. You can make an interesting image from literally anything. I've worked with seed images that are literally just random dots and created interesting patterns. This creates an interesting aesthetic problem - which among all the interesting pictures is the best?
What do you think?
I present regular philosophy discussions in a virtual reality called Second Life.
I set a topic and people come as avatars and sit around a virtual table to discuss it.
Each week I write a short essay to set the topic.
I show a selection of them here.