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Mandelbrot

Introduction

Mandelbrot is an app for Android for drawing a Mandelbrot set. Zoom in or out and change the colors accordingly to your imagination. Save the calculation parameters or the complete picture to see it later again.

The app is available in Google App-Store or in Amazon App-Store.

Main View

In the main view, the calculation process for drawing the Mandelbrot set is started. Simply press RUN. You can move and zoom the displayed area with your fingers.

Depending on the size of the screen, you will find important functions directly above, the rest are in the menu.

Menu item	Description
Run	Starts the calculation and display the Mandelbrot set.
Stop	Stops the calculation. A continuation is not possible. Instead, restart completely.
Zoom in	Starts the calculation again with the middle area, so that finer details can be seen. The middle area is shown enlarged.
Zoom out	Shows a larger range of the Mandelbrot set, i.e. additional areas from outside the previous presentation. The previous view is reduced in size.
Continue	Performs the paused calculation.
Suspend	Holds the current calculation, a continuation is possible.
Picture Settings	Set the size of the calculated image.
Calculation Settings	Set the calculated range of the Mandelbrot set and the limits for the iteration.
Colors	Definition of the color scheme used.
Save Picture	Saves the generated image as jpg- or png-file. This can be displayed with any image viewer.
Load Picture	Loads an image to view.
Save Calculation Parameters	Saves the parameters of the calculation including colors. The calculation can be repeated with the parameter file. The parameter file is usually much smaller than the image file. If it is sent by mail, the recipient also needs the Mandelbrot app.
Load Calculation Parameters	Loads a parameter file to recalculate an image.
Restore original configuration	Restores the original state of the calculated section of the Mandelbrot set as well as the color scheme.
Add to Batch	Adds the current computation parameters, i.e. the section of the Mandelbrot set, and the color scheme to the batch parameters.
Edit Batch	With a batch, several areas of the Mandelbrot set and intermediate images can be calculated automatically. These frames can be used to create a movie. The app calculates only the single images, it can not create an MPEG movie directly.
Preview Batch	The images defined in the batch are calculated and displayed so that the sequence of the scenes can be checked. No intermediate images are calculated.
Run Batch	The images and intermediate images are calculated and displayed. If activated, the images are also stored with automatic numbering.
Show Homepage	Displays the homepage where this manual is located.
Exit	Ends the app. You can also press the app icon in the upper left corner to exit.

Picture Settings

The size of the calculated image can be set in the picture settings. In addition, the calculation for acceleration can be divided into several areas.

Calculation Settings

The arithmetic parameters x and y determine the range of the Mandelbrot set to be calculated and displayed. This area can be set more intuitively by moving and zooming the image with the fingers in the main view. The values can then be read here.

The maximum iterations and boundary value affect the calculation. The calculation is a recursive process whose number of runs is counted. The recursion is terminated when either the boundary value has been exceeded or the maximum number of iterations. The higher the number of iterations, the more details are displayed. On the other side the calculation time rise. Selecting Fine leading to finer color transitions. Examples of the effects of these parameters are shown below.

Color Settings

In the color settings, you can select a color scheme from a given list or define your own color scheme as a custom color scheme. With the menu item Restore you can reset the color scheme to the state it had when calling the mask.

A custom color scheme can also be stored in a file or loaded from a file. For a custom color scheme, you can select a color from a palette by pressing the color rectangle or selecting Select Color from the menu. Alternatively, the RGB values can be set between 0 and 255.

The number of iterations is counted in the calculation process of the Mandelbrot set. The number determines with the entry from index the displayed color. Possibly the color is interpolated from two color lines. If the number of iterations is greater than the last index entry, only the last color would be displayed. In order to avoid having to extend the color definition, the color definition can be automatically repeated using the Auto extend selection field.

File Dialog

The file dialog is used to select a filename to load or store images, colors, and parameter files in multiple menu entries. It is possible to select the internal application directory and, if available, the SD card. Files and directories can be created and deleted. To change into a directory please press the directory for a long time. To change to the parent directory, please select Up in the menu.

The file type is preset according to the purpose of the file. The current directory is displayed under the filename. Among the files and sub directories in the current directory are listed.

Batch Definition

A sequence of images can be defined in the batch definition. A number of intermediate images can be automatically calculated between two defined images. This gives the individual images to a film. However, the app does not produce a movie file. For this purpose, further software is required, e.g. a video editing program. The calculation of the intermediate images can be influenced by the move mode.

The zoom info field shows the zoom factor to the next defined image and is used for orientation. The selected entry also serves as the start of the calculation. To calculate everything, the entry index 0 must be selected before exiting the mask.

The Fine mode

The number of iterations is counted in the calculation of the Mandelbrot set. This is an integer. This sometimes leads to staged colors.

By setting Fine, the number of iterations becomes a number with decimal places, which makes the color transitions finer.

Iterations and Colors

The following color definition was used for the following examples. Depending on the number of iterations in the calculation, a point in the image is displayed in the corresponding color. For example, 20 iterations as green and at 30 as yellow. At 25, a mixed color of green and yellow would be displayed. The color table is designed for a maximum of 200 iterations. By automatic expansion, however, it can also be used for higher numbers of iterations.

For the two following images, the maximum number of iterations was 150. In the color definition 150 is a color between white and dark blue, thus a light blue. The first image is without automatic color extension and the second one with. However, since 150 is within the color definition, the automatic color enhancement is not used so that both images are the same.

The two following images use a maximum number of iterations of 200, again without and with automatic color extension. The color definition is now fully utilized, some areas of the images are black. Since 200 is also just within the color definition, the automatic color enhancement is also not used, so both images are the same.

For the following images, the maximum number of iterations is 600, again without and with automatic color extension. The image without automatic color extension shows no difference to the image with 200 iterations. All values above 200 are also mapped to the highest entry 200 of the color definition, that is, shown as black. On the other hand, formerly black areas are displayed in other colors in the image with automatic color extension since the values over 200 are automatically distributed over the color definition.

The following images have a maximum number of iterations of 800 and 950, both with automatic color extension. The higher the maximum number of iterations, the more details you see in previously empty areas.

Permission for SD card

Depending on the Android version, it may be necessary to assign a permission for the SD card if you want to load or store your own image. Depending on the Android version and manufacturer, the following images may look different. First, please go to the Android settings and then switch to the apps.

Then press the desired app and select Permissions there.

Finally allow access to Storage.