Julia Fractal
Julia applet.
Instructions: To zoom in on an area, highlight it with mouse by dragging out a rectangle. To zoom out press reset button. You can change intensity of light using '-/+' buttons.
Description:
This fractal was named for mathematician Gaston Julia (1893-1978). It is generated by following algorithm:
Zn+1 = Z2n + C
where:
C = Re(C)+i*Im(C), Re(C) and Im(C) are constants,
initial value of Z = (x-coordinate) + i*(y-coordinate)
This algorithm is similar to algoritm to generate Mandelbrot sets. There is a Julia set corresponding to every point on the complex plane (an infinite number of Julia sets). The most visually attractive Julia sets tend to be found for the C values equal to points of the Mandelbrot set just outside the boundary. If the points are far inside the boundary the corresponding Julia set will be a circle. If the points are too far outside the boundary Julia sets break into scattered points.
Historically, the Julia sets came first. It was a while looking at the Mandelbrot set as an "index" of all the Julia sets' origins that Mandelbrot noticed its properites.
Connection between Julia and Mandelbrot set
Julia set with different colour schemes.
Julia set of higher orders.
Back to main page