The equations that generate fractals, however, are nonlinear. Nonlinear equations involve iteration, which means that the solution of the equation is repeatedly fed back into itself. It is an ...

Many fractals, like the Mandelbrot set above, come from intricate mathematical equations. But some are much simpler and easier to construct. One straightforward but still fascinating fractal is ...

By folding fractals into 3-D objects, a mathematical duo hopes to gain new insight into simple equations. Ordinary equations can be transformed into complex 3-D figures that offer new questions to ...

The most famous fractal equation is the 2D Mandelbrot set, named after the mathematician Benoît Mandelbrot of Yale University, who coined the name “fractals” for the resulting shapes in 1975 ...

Crop circle designs containing fractal patterns (such as the Mandelbrot set) have been created for many years. ... A mathematical equation, on the other hand, requires intelligence.

Fractal-Generating Software: Programs like Apophysis and Ultra Fractal allow artists to produce fractal images by manipulating mathematical parameters. Online Equation Editors: Platforms such as ...

The quest by a group of math geeks to create a three-dimensional analogue for the mesmerizing Mandelbrot fractal has ended in success. They call it the Mandelbulb. The 3-D renderings were ...

The exhibit uses fractals -- mathematical equations represented as infinitely repeating shapes and patterns. Horsthuis runs the equations through the software Mandelbulb 3D, which then manifests ...