Math never looked so good as with a funky new language that produces color-by-the-numbers images as it tries to define nature.
Fractal geometry is a home-grown language in mathematics that helps define the undefinable - the measurements of clouds, mountains and stars.Fractals are plugged into the computer, which is where the art comes up, said Heinz-Otto Peitgen, mathematics professor at the University of Bremen in West Germany and the University of California at Santa Cruz.
"Geometry, in the first place, is a language, like English is a language to communicate in this country," said the German-born Peitgen. "Geometry is a language to communicate in the sciences.
"It's a new language to describe nature," he said, adding the traditional squares, cubes and lines of geometry "although at the basis of modern science, is not adequate or suitable to describe the elements of nature."
Peitgen came up with the concept while on sabbatical in Utah, after a discussion with another researcher regarding turbulence. He headed to the computer to resolve his questions.
The University of Utah at that time had one of the few very sophisticated computers to map out the problems the professor had, said Klaus Schmitt, mathematics department chairman and Peitgen's collaborator.
Mathematicians discuss mapping turbulence or flows. What fractal geometry produces is a freeze-frame picture of turbulence, said Schmitt. "The swirls you see would evolve like an eddy."
Because there is no language to communicate what is going on within turbulence found in clouds or in a pool of water, it seems logical to go to a computer to map it out.
"Fractals in a sense are just bringing into science what lay people have somehow felt all the time," said Peitgen.
The professor said a mathematician using fractals can define lightning in the same fashion landscape planners can define slopes.
"Fractal geometry is now able to talk about the architecture of a cloud as accurately as an architect can talk about the geometry of a house," said Peitgen.
"It's not a question of imagination. It's a possibility of adding a new language to the world to define the complexities of nature."
In the process of explaining the complexities and dimensions, "we use the computer to get some intuition. The computer helps us go into worlds of complexity that are just beyond any human imagination."
The swirling lines and images are reminiscent of the Peter Max art of the 1960s. The flowing colors and shapes have lent themselves to advertising and interior decorating.
"It's hot, it's evolving, it's happening in the sciences right now," said Peitgen.
Peitgen's book, The Beauty of Fractals, won the 1987 award for Distinguished Technical Communication. An exhibit of his work, Frontiers of Chaos, is traveling the globe under the sponsorship of the Goethe Institute, an organization that promotes cultural cooperation.
The attractive language also can help entice children into the world of science.
Schmitt travels to schools around the Salt Lake Valley with his computer to show children the excitement of mathematics in a way they've never seen.
"Many of the high school kids are interested in it too. They are just fascinated by this whole stuff," said Schmitt. "It just turns them on."
"Children who didn't like geometry in education didn't like it because geometry is such a removed, abstract thing," Peitgen said. The shapes were forms children "didn't really see in the world."
But fractal images are "much closer to nature," said Peitgen. "Just by looking at the pictures you're intrigued. This is not changing mathematics. At least it gives a beautiful new way of looking at things."
Fractals filled in some blanks within the mathematical language, allowing economists, architects and biologists new capacity for understanding. The language allows use of right-now tools as opposed to something 2,000 years old.
The language also allows people of different cultures to communicate.
"These images for some reason have been appreciated around the world," said Peitgen. "That tells me something about this.
"I think that message is best explained by reminding yourself no matter where you are - China, Japan, America - if you see a tree and a nice blue sky behind the tree, regardless of what your culture is, you're going to see this as nice."
A show on computers and art just closed at the Salt Lake Arts Center, and Peitgen and Benoit Mandelbrot, a scientist who coined the term fractals, were featured on an episode of "The Nature of Things" on Public Broadcasting Service.