Explore Mandelbrot's Set with zExplorer
||What is Mandelbrot's Set.|
This is the set of numbers which are stable under successive transformations by the relationship zn = zn-12+c. The set of numbers is an area in 2D which is displayed in white, the edge of the area is a fractal - a curve of infinite length. With zExplorer you can discover the beauty of fractals and their amazing properties.
The colours represent the number of transformations required to reject a number from the Set. White numbers are never rejected, purple numbers require fewer transformations, passing through blue, green, yellow and red with the highest number of transformations.
How to use zExplorer.
To explore a new region, drag a rectangular box around it with the mouse and hit run.
You can select a new region whenever you wish (you don't have to wait until the image has finished processing). Adjust the parameter values as required and hit the return key to apply them immediately.
- resolution is the number of transformations used to determine the fractal.
Higher values give better definition, but take longer.
- dot pitch is the number of screen pixels between points, 1 is the actual screen resolution. Use larger numbers to produce coarser (faster) images
as you explore, and smaller numbers to see the detail.
- zoom is the zoom factor for the zoomout button, the window size is increased
by that amount.
- colours is the number of colours used to map the points, arranged by hue.
- origin is the position of the centre of the window in x-y coordinates.
- size is the size of the window in x coordinates. Note the whole of Mandelbrot's set
fits inside a 1.5 by 1.5 area. You can explore down to 0.00000000001 areas with zExplorer.
- image is the current image in the history list, up to 20 images will be stored. Use > and < to go forwards and backwards. Note the selection rectangle applies to the latest image in the list only (this feature may be improved in later versions).
First edition at 26.11.97 (c) S.J.O'Connor 1997
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