Below the image are six options that display different sets of controls to manipulate the image. Click on one of these to display those controls. They are:
|Mode:|| There are two sets of options here.
|Explore:|| Once you have chosen the pattern and the mode of coloring you can pan around the image and move in
and out. There are three sections.
This allows you to adjust the colouring parameters within the five colouring modes introduced in the "Mode" section. There are 4 adjustable parameters:
The equation we are iterating, z → z = zn + c, has four potential variables, Zx, Zy, Cx and Cy.
When we create one of these fractal images we keep two of these constant and vary the two others over the range of value that defines the view are that we see on the screen.
To draw the standard Mandelbrot we set (Zx,Zy) to (0,0) and vary (Cx,Cy) over the view window.
To draw a Julia set we set (Cx,Cy) to a constant value and then vary the starting Z value (Zx,Zy) over the view window. When you choose the Julia plane the (Cx,Cy) value will be the centre point of the Mandelbrot image. If you pan around the Julia set and then switch back to the Mandelbrot plane the image will be constructed with the initial Z value being the centre of the Julia image. This will dispay a plane that is parallel to the standard Mandelbrot set but offset by the vector (0,0,Zx,Zy).
If you imagine the (Cx,Cy,Zx,Zy) as defining a 4-dimensional space then there are 4 other planes orthogonal to the Mandelbrot and Julia planes. You can view what the set looks like in these planes and pan around them. The caption immediately below the image will tell you where you are in this 4-D space.
This allows you to change the initial values of Z0 and C0. Changing 'Z' will have no effect on the Julia sets and changing 'C' no effect on the Mandelbrots.
This allows you to change the floating point precission value passed to the WebGL shaders. I was hoping that this would enable deeper zooms, but it appears to make no difference on any graphics card I've tried. Maybe I'm not doing it right.
(c) John Whitehouse 2015-2017