IBlog: Sujeet Lahane

On the Julia Sets

The inception of Julia Sets lie in a very simple mathematical equation,

Z = Z² + c,
where, Z, c \( \in \mathbb{C}\)

in its iterative form, this is written as,

Z _i+1 = Z_i² + c, i = \(0, 1, 2, \)...

The Julia set is the set of Z\(_0\)'s for which Z_i is bounded under a fixed c.

Another set that arises from the equation is a Mandelbrot set. In Mandelbrot set the Z\(_0\) is set to 0, and is a set of c's for which Z_i is bounded.

In popular science you might have seen beautiful visualizations of any of these two sets. The colors in such visualizations describe of how many iterations of this equation are required for Z_i to attain values beyond a fixed bound.

To be Updated