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Hans S. Kim | profile | all galleries >> Mandeldrot Fractal Pictures tree view | thumbnails | slideshow

Mandeldrot Fractal Pictures

Computer generated fractal images. These are Mandeldrot images from mathmetical function (x - yi)^z. Exponent z is the value that plots the color of each pixel in the picture. i is an imaginary number(square root of -1). i^2 is -1 and i^3 is -i and i^4 is 1 and so on. You set a limit for z like somthing equal to or greater than 400 and you calulate the function until the value of the function reaches 4.0. Then you take the z value, number of iteration, and divide it by the number of colors that you are using for the picture. For instance in these pictures I used 1024 colors. So you divide the z by 1024 and take the remainder of the division and use it as the color index to plot the x and y point. If z reaches 400 or whatever the max iteration count is and the value of the function still did not reach 4.0 then you put a black pixel for that point(x,y). x and y is a floting point number that is mapped to the physical screen. If you set the picture size to 1200x900 and horizontal mapping goes from -2.0 to 2.0 and vertical mapping also goes from -2.0 to 2.0 than 0 is -2.0 and 1200 is 2.0 for x and 0 is -2.0 and 900 is 2.0 for y. Some of these pictures are points ploted in 1 billionth of and area. Most beatiful pictures are in the range of 1000th to millionth.
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