England Annexes Neighbor ?

Fractal geometry is able to interpret irregular shapes like mountain ranges, coastlines and banks of clouds and describe them in mathematical terms. When this idea was first published in 1967 by Benoit Mandelbrot the term fractal had not yet been coined. The term fractal came from Mandelbrot in 1975 and has come to mean an object characterized by the repetition of similar patterns at ever diminishing scales. You will see why in a moment in this classic example. Imagine wanting to know the length of the coastline of Britain. Using Euclidean geometry a fairly straight outline of Britain would be used to find the perimeter of the island and it would be approximately 2400 km. Fractal geometry will measure the coastline using ever decreasing units of measure so that the resulting measurement will include all the nooks and crannies that make the true perimeter of the island and the coast is approximately 3400 km.  No, Britain did not annex a neighbor’s coast to generate the extra 1,000 km. Instead, all the little fractions, or fractals, of the coast are included in the measurement. These nooks and crannies are referred to as self-similar in fractal terms. This means the coastline repeats a pattern of nooks and crannies at ever diminishing scales. In the case of the coast, the small little bays are very similar to the next larger bay and that bay is shaped a lot like the bigger bay it is a part of and so on.

2400 km versus 3400 km

Blew me away

The next two pieces I am very excited about. The first and smaller piece is done on clayboard. (I usually use synthetic paper.) Normally I paint a sheet of plexiglass and they lay my painting surface on top. This time I painted the board and then laid a light weight piece of flex-o-pane on top. My usual techniques of separation did not work with the light plastic so I dragged out my air compressor. I cut small slits to insert the air tube and turned on the power. I am very excited by the results.

Hansel, 8 x 10 clayboard with acrylic paint.

So then….

I cut a piece of flex-o-pane to lay over my synthetic paper. I put a couple of small slits in it for the compressor tube. Then I painted my paper, laid the plastic pane on top and made sure there was good contact. The tube was inserted and the power turned on. I moved the hose around a bit and switched slits once. I used some bamboo skewers to help hold the plastic up off the already printed area. I will try this again!!!

Fuchsia, 20 x 26, acrylic on synthetic paper.

I am not sure that ‘Fuchsia’ is the correct title. I am open to suggestions.

Off Topic

I have been posting thoughts from my fractal thesis, but today, I want to share some new techniques I am working on.

The first two pieces are inspired by the fractal dimension. The fractal dimension is a state of drawing or painting that in neither 1 dimensional or 2 dimensional. It lives around 1.6 and 1.7. Jackson Pollock’s drip paintings often fall in this category. It is why we enjoy looking at them. Our brains just love the complexity. So, my thought was to lay string in the wet paint.

What? String you say….

The plan was to begin my piece the usual way, by pressing paint between two smooth surfaces. Once the two surfaces were removed, I would lay string on the still wet paint, return the second surface and print a second time. I was hoping to get a multi-dimensional result. A little like a pile of cooked spaghetti. I did NOT get what I was hoping for but found the result to be interesting.

Amoeba, 26 x 20 inches, acrylic on synthetic paper
Snakes, 20 x 26 inches, acrylic on synthetic paper.

What? A Fractal!

One a month is not enough. You will hear from me twice a month.

The discovery of the fractal and fractal geometry is considered by many to be one of the important discoveries of our time, yet most of us are unfamiliar with what a fractal is. The simplest and most basic description of a fractal is an object characterized by the repetition of similar patterns at ever diminishing scales. A fern is an excellent example of a natural fractal. Each small leaflet is similar in shape to the branch it is a part of and the branch resembles the entire plant.

We are not only unfamiliar with what fractals are but how their geometry can be applied. It has applications in a myriad of disciplines. Scientists use fractal geometry in medicine, predictive geology and botany. Engineers and mathematicians use it for computer algorithms and in manufacturing. Economists use fractal geometry in chaos theory and therefore predictive modeling. Social scientists use fractal geometry to explain the behavior of cultures and their development. Contemporary computer artists generate beautiful, complex fractal images.

This blog will familiarize you with fractals and how to identify them. You will learn the five components of a fractal. Then you will see how artists use fractals and how fractals can relate math to our everyday environment.

Blog Posts

Once a month I will send out a fascinating email that will give you new and interesting information about fractals.

The majority of these posts will draw from my thesis, “The Art of Fractals for the Mathematically Challenged”. I am fascinated with fractals but by no means can compute the math.

Blog 1…. here we go!!

One of the most difficult things about being an artist is coming up with new and interesting ideas that are engaging to work on that are artistic and emotional things of beauty. This means that searching for inspiration in an ongoing endeavor for most artists. It was during one such search that I stumbled upon a fractal. There it was on my computer screen, a thing of beauty. I had never seen one and had no idea of how it was created. I wanted, I needed,  to know more. Thus began an ongoing exploration into what many consider to be one of the most significant discoveries of our time, the fractal and fractal geometry. The purpose of this blog is to explain what a fractal is, what they can do, why we like them, where they are found and their effects on the world of art.