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Fractals

About fractals and the parameters for the Fractal Designer


A fractal is an image that is generated by use of a mathematical formula. The resulting design can be very intricate and elegant. The Fractal Designer (a Shockwave application) lets you create a fractal. You can change the parameters of the mathematical formula, thus changing the resulting design. The application uses two formulas that you can choose from:
      Mandelbrot       Julia

The Mandelbrot formula has four parameters that you can set:
      crMin     crMax     ciMin     ciMax
You can enter values between -2 and +2. They define the boundaries of the fractal. The smaller the values, the more you zoom in to an area.

The Julia formula has two extra parameters (in addition to the four parameters for the Mandelbrot formula) that you can set:
      crConst     ciConst
You can enter values between -2 and +2. They define a point in the complex plane of a mandelbrot fractal.

Additionaly, you can set the maximum number of iterations that is used for the calculation of the color of each image-point of the fractal. This number is equal to the number of colors that will be displayed in the fractal.
      Number of iterations / colors
You can enter values between 2 and 254. The higher the number, the more colorfull and detailed the final image will be, but also the longer it will take to calculate.

There are 9 presets.
      Presets
If you select any of the numbered presets, the application will use predefined values for the parameters.

Once you have chosen your parameters, you can select the Go! button, and the corresponding fractal will be calculated. First you will see little detail, but as the calculation continous, more detail will be added. You can follow the process by the information that is displayed:
On the top of the window is a line "Block size = .. pixels". This shows the size of the color elements that are being calculated.
On the bottom of the window is a line "Row .. of ..". This shows the row (from top to bottom) that is being worked on.
On the right is a colored bar that shows the progress of the calculation. When the bar is all green, the calculation is finished. Next to the bar are two numbers that indicate the time in seconds. The number at the bottom left of the bar gives the time used sofar. The number at the top left of the bar gives the estimated total time that is needed to complete the fractal.

If you click somewhere on the fractal window, you will zoom in to that particular area.
If you control-click you will zoom out.

To the left of the window are 7 small color palette buttons. Clicking any of them will change the available colors for the fractal and restart the calculation. The 7 color palettes are from top to bottom:
      system     rainbow     grayscale     pastels     vivid     ntsc     metallic
The system palette is the default one. This one contains a rather random selection of colors, resulting in rather chaotic looking fractals. The other palettes are more ordered and create more gradually changing fractals.

If you click on the letter R in the bottom left corner, you will Restart the calculation. If you click on the letter C in the bottom right corner, you will be able to Change the parameters for a new calculation. If you click on the letter Q in the top right corner, you will Quit the application.


Fractals

image created with the fractal designer
Launch the fractal designer

You need the Shockwave plugin and javascript enabled.