Patterns
There has been an intense fixation in both mathematics and art over the observation and creation of patterns. In art, being able to recognize a pattern allows connections to be drawn between seemingly different things.
On one hand, patterns allow you to differentiate between background and figure, on the other hand, patterns can be used as distraction or camouflage to disguise a subject matter or figure.
By noticing subtle differences in varying things, an observer can learn relations between those differing things; artists take note by imitating or copying these patterns, while mathematicians and scientists count, replicate and record these patterns of difference.
'Set of Rules'
The images that artists make inspired by patterns have the capacity to resemble the 'big idea' that reveals the relationship between the parts. Patterns in art bring a certain understanding of structure, grasped by the artist, and made to be shared with others. In mathematics, the abstract qualities of the pattern become measurable, and an accurate understanding can be discovered when the numbers that represent the pattern are digested and analyzed.
Patterns use qualities of color and location, in combination, to create an image.
In a used bookstore I found a gem of a book that explores these very same ideas of patterns in geometry and color, and utilize computer software to put patterns of mathematics to the test to create images.
Symmetry in Chaos
Michael Field and Martin Golubitsky's Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature (1992) features large full-color images showing infinitely varying blossoms of color and forms, the product of formulas for geometries found naturally in the structures of nature and rendered with a computer.
The book explains how natural symmetries in nature and the undeniable tendency towards complexity found in the world around us, can be translated into computer script and tested to make similarly striking and symmetrical images that are both unique and appealing.
Using formulas, there is both an input of varying settings, and an output, being a determined point on a grid. For an image to form, the process must be repeat many times, several million iterations, to create images like these.
The software comes with two main categories outlined in the book: the first are called Icons and are complete and centralized patterns that often follow symmetries within itself. The second are Quilts, which are essentially the same as Icons but are seamless and follow patterns that have no defined border and can be repeated indefinitely.
Initially, I was trying to find my own way to write script for the software, as there a was simple guide in the back of the book. Me being a visual artist, not a digital programmer, failed at this.
Only afterward was I lucky enough to stumble upon a peer's website with an already created program of the same processes and parameters from the book done by Jim Burgess.
While it seems to not have been touched since 2004 (outdated by cyber standards, but not nearly as antiquated as the book which inspired the program), fortunately the software still functioned on my computer and I was soon making my own symmetric images!
The Icon Program is free to use and is what allowed me to create these images with little to no time and minimal frustration and effort.
Mathematical Visual Generator
How It Works
With changeable parameters and five variables to alter, the computer calculates a formula that has varying outcomes. One calculation would not reveal much besides a point on a graph, but when repeated thousands of iterations, the points begin to fill the empty spaces, as well as has a chance to land in the same places multiple times. (Field and Golubitz, 28.)
The computer does this 6 or 8 million iterations to make a detailed and information-rich image. The software then assigns colors according to how many times a point landed in each spot. The spectrum of the software shows low amounts of points as cool blue, and goes through to warm colors accordingly with more repetition. Red, Orange and Yellow areas are more likely have a point dropped there, while some areas are dark without any points.
This is why computers become the ideal tool, because without them it would take years to plot so many points on a grid.
This process of image making is directly influenced by the mathematics but as a software is a tool to make symmetrical images that share natural organic qualities but are completely digital.
How It Changes
What is most exciting to me is how the software can allow me to experiment on a plane that exercises both the logical and mathematical left, and creative and visual right hemisphere of the brain, in a unified way. Seeing both a calculable indicator and visual rendering makes the action of changing and tweaking settings more engaging in a way I can't relate in words.
Once captured as a digital file, the patterns and icon images are easily edited in Adobe Photoshop and created into new outcomes. I later edited them and printed digital negatives to be used for printing Van Dyke Brown photographs.
Potential in Art
Creating patterns and repeating forms is essential to any large piece of artwork, and I so I think this software tool will allow me to create buffer zones of intricate and intriguing patterns, without spending countless hours repeating these forms by hand. It allows me to alter digital images that can then be transposed onto paper and Van dyke brown prints and exist as a material images, in a way not originally intended.
I love how they play in the mysterious zone between traditional photography, and newer computer generated images in a way that makes them both seem organic and never conflicted.
Printing with Pattern
Whats really fascinating is how similar this process of creating an image on the Icon software is to actual photographing.
When I print outside using ultraviolet sunlight to expose photographs, there is a similar process going on. While in the software the computer calculates and plots a single point at a time and repeats this numerous times, so do single photons of light individually hit the photographic paper and react with the silver nitrate, but all at once.
The more photons hit in one single spot, the darker that spot gets when developed. Similarly the computer interprets multiple points as being 'hotter' and knows to give a brighter color according to that amount of points. The more hits of the point, or the photon, both result in an intensity of pigment.
The calculations sometimes miss whole spots of the canvas as they follow the mathematical patterns. Likewise the sunlight misses some spots on the photograph where it doesn't react, because there is a negative-image over it, blocking some of the photons.
There is a direct relation between the density of pigment (determined by the artist) on this negative, and the amount of light that gets through. Likewise there is a direct relation between the parameters (determined by the mathematics) and the density of points of the graph.
It is as if these two processes reveal a deeper understanding as to what is needed to compose an image, and how the individual units and their intensity are essential to what composes of that image. The two processes of image-making seem to compliment each other in a way that brings new insight into some of my art and the underlying structure that builds our world.
Mathematics plays a role in much art, but it is often ruined by focusing on extensive art theory and planar analysis. In this case the mathematics are just as thrilling and uncertain as other art-making, just as surprising, and I'm delighted to share it with everyone.
1.Field and Golubitsky, Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature. Oxford: Oxford University Press. 1992.
Finished collage exclusively using imagery created with the Icon software and mathematical formulas from Geometries in Chaos.
Micron, 2017. Van Dyke Brown Collage (12"x 12")