A Playground of Thoughts > Mandelbrot Microscope

## Mandelbrot Microscope

**How to use:**

This program shows images of Mandelbrot Set and Julia Sets.

The choice box allows you to choose either Mandelbrot Set or Julia Set.

**Center x** and **Center y** determines the center of the image on Gaussian plane, and **Radius** determines the radius of the image.

To get more precise image of the border of Mandelbrot Set, increase the **Iteration** value.

**Julia x** and **Julia y** determines the factor of Julia Set. (**z**_{j} in the formula described later.) These two parameters have no effect on Mandelbrot Set.

The **Load** button sets **Julia x** and **Julia y** to the values of **Center x** and **Center y** respectively.

To zoom up the area you want to see pricisely, drag the mouse to select the area or set appropriate values and press the **Go** button.

The ESC key cancels the mouse drag.

Arrow keys allow you to move the center. Hit 'z' to zoom in, 'p' to zoom out.

Mandelbrot Set is defined by the following formula:

**z**_{0} = **x** + **y** i

`z`_{n + 1} = **z**_{n}^{2} + **z**_{0}

Mandelbrot Set = { **z**_{0} | abs(**z**_{infinity}) < infinity }

Julia Sets are similar to Mandelbrot Set. The Julia Set for **z**_{j} is defined as follows:

**z**_{0} = **x** + **y** i

**z**_{j} = **x**_{j} + **y**_{j} i

`z`_{n + 1} = **z**_{n}^{2} + **z**_{j}

Julia Set = { **z**_{0} | abs(**z**_{infinity}) < infinity }

This Java applet needs Java 1.1 or later.

The main characteristic of this Mandelbrot Set viewer is its gradual coloring. Other Mandelbrot Set viewers feature more functions, but they often produce less aesthetic images.

Some browsers cannot display colors properly.

The source of Mandelbrot.class

The source of Bitmap.class

The source of BitmapInputStream.class

The source of BitmapOutputStream.class

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Copyright(C) TAKASUGI Shinji (tssf.airnet.ne.jp)