User-defined content

Custom palettes

Use the add button on Custom tab of the palette list to create your custom palette.

A palette consists of 10 color entries, some of them may be empty. A palette is a cycle so it ends with a transition from the last defined color to the first one. You should define at least two entries including the first one which can not be empty.

Empty slots are indicated by icon. Tap a slot to set or change its color using an HSL color picker. The picker displays RBG color number and you may tap that number to input RGB color value with a keyboard.

Tap a bin icon to delete an entry.

Use the Randomize button to let the app generating a random palette for you.

Enter a unique name for your palette before saving it.

You may later change your palette by long-pressing it on the palette list and choosing the Edit option from its context menu.

Custom fractal types

The app lets you create custom fractal types using formulas or short programs written in the app's embedded MbLan expression language. The app uses MbLan virtual machine for computing custom fractals. This works slower than computing built-in fractals that have a native RenderScript implementation.

To take full advantage of defining custom fractals, it may be useful to read the Computing fractal images page of this tutorial.

Use the add button on the Custom tab of the fractal types list to create your custom fractal type.

First, choose a definition type:

Simple (formula) Define a fractal by giving a formula.
Advanced (program) Define a fractal by completing a short program. It gives you more control but may require some programming background.

Creating simple and advanced fractal definitions is described in the following sections.

You may use the built-in fractal types definitions as examples. You can clone a built-in definition and modify it to create your custom fractal type. Long press the item on the fractal types list and choose the Clone option from its context menu.

In the app's free version you may create one custom fractal type. Unlock Premium to create any number of them.

Simple fractal definition

A new simple fractal definition is initialized to compute the classic Mandelbrot Set fractal.

Give a unique name to your custom fractal and change at least the fractal formula.

Escape

Condition type used to break the iteration. The default DIVERGENCE escape is good for most of polynomial based fractal formulas. For root-finding fractals, CONVERGENCE escape is more suitable.

Seed

An initial value for applying a fractal formula (a complex type expression).

In most cases, the default value of 0 is good enough.

For root-finding fractals, the current point value c is often used as the seed.

Fractal formula

A complex type expression that will be repeatedly applied to the initial value.

You may refer to the value of previous element z and the current point value c.

For more information on writing formulas, see the MbLan expression language reference.

Parameters

See the Custom parameters section.

Advanced fractal definition

An advanced definition screen displays a short program computing the fractal for the given current point value c. Most of the program (including the loop) is fixed and you only need to complete the fragments computing the subsequent values. See MbLan expression language for more information on the syntax.

A new advanced fractal definition is initialized to compute the classic Mandelbrot Set fractal.

Escape

Condition type used to break the iteration. In addition to the built-in types described in the Simple fractal definition section, you may choose CUSTOM which allows you to define your escape condition by writing:

if (your condition) break;

at the beginning of the iteration code section (see built-in Collatz fractal definition for an example).

The fixed part of the program automatically changes to reflect the chosen escape type in a loop condition. This shows you how exactly the built-in conditions work.

Smooth

Formula type used for smoothing the resulting image. In most cases, you may just leave the default BUILT-IN formula which is good for the built-in DIVERGENCE and CONVERGENCE escape conditions.

Choose CUSTOM for writing your smooth formula in the Finalize code section and assigning the calculated smooth factor value to the built-in variable smooth.

The smooth variable initial value is 1, so if you choose CUSTOM smooth and do not assign other value then your fractal type will not support smoothing.

You must choose CUSTOM smooth when using CUSTOM escape condition. See built-in Collatz fractal definition for an example.

The fixed part of the program automatically changes to reflect the chosen smooth type and escape type. This shows you how the built-in smooth formulas work.

Initialization code

You may set the initial value (the built-in variable z) and the bailout value (the built-in variable bailout).

These values are initialized in the fixed part of the program so you may leave the section empty if you do not want to change them. The default initial value is 0. The default bailout value is 2e+8 for DIVERGENCE or CUSTOM escape, and 1e-14 for CONVERGENCE escape.

When using the BUILT-IN smooth with DIVERGENCE escape you should also assign a value to the exponent variable which is used for computing a smooth factor. For simple polynomial formulas, this should be the highest exponent of z in the formula. More information can be found in the Smoothing for DIVERGENCE escape section.

In this section, you may declare your helper variables and give them initial values. Variables declaration must be at the very beginning of the section.

Iteration code

This is the most important section where the next value is computed. You should at least give a new value to the built-in variable z.

For CUSTOM escape type you should check your escape condition, and when it occurs, use break; instruction to stop the iteration.

Finalize code

In most cases, you may leave this section empty unless you use CUSTOM smooth type or you want to do some tricks (see built-in Lyapunov fractal definition for an example).

Parameters

See the Custom parameters section.

Custom paint modes

As a result of repeatedly applying the fractal formula to the given initial value, we get a sequence of complex numbers called an orbit. A paint mode is a way of transforming the orbit into one value (called a paint value) which is mapped to color from a palette. More detailed information can be found in the Coloring techniques section.

The app lets you create custom paint modes using formulas or short programs written in the app's embedded MbLan expression language. The app uses MbLan virtual machine for computing custom paint modes. This works slower than computing built-in paint modes that have a native RenderScript implementation.

Use the add button on the Custom tab of the paint mode list to create your custom paint mode.

First, choose a definition type:

Simple (formula) Define a paint mode by giving a formula.
Advanced (program) Define a paint mode by completing a short program. It gives you more control but may require some programming background.

Creating simple and advanced definitions is described in the following sections.

You may use the built-in paint modes definitions as examples. You can clone a built-in definition and modify it to create your custom paint mode.

In the app's free version you may create one custom paint mode. Unlock Premium to create any number of them.

Simple paint mode definition

A simple definition paint mode applies the given formula to each orbit element and then aggregates the resulting values by taking their average, minimal or maximal value.

A new simple paint mode definition is initialized as a clone of the built-in Foggy paint mode without the Pattern intensity parameter.

Give a unique name to your custom paint mode and change at least the paint mode formula.

Aggregation

Choose an aggregation method. The simplest are AVG(value), MIN(value) and MAX(value), which simply take average, minimal or maximal value of the formula.

The app also offers more complex methods that transform the values before aggregating them. Different methods can give different images but not all will be interesting for a particular spot.

The default method AVG(1/(1+abs(value))) gives good results in most cases, so please use it for your first custom paint modes.

You could easily include a value transformation in a paint mode formula but using a built-in transformation is more convenient and the image will be rendered a little bit faster because of the native implementation.

Paint mode formula

A complex type expression computing a value for an orbit element.

You may refer to the value of the element z and the current point value c.

For more information on writing formulas, see the MbLan expression language reference.

Parameters

See the Custom parameters section.

Advanced paint mode definition

An advanced definition screen displays a short program calculating the value that will be mapped to color. Most of the program (including the loop) is fixed and you only need to complete the fragments computing a paint value.

The program is initialized to compute the built-in Foggy paint mode.

Aggregation

Choose an aggregation method.

In addition to methods described in the Simple paint mode section, you may choose CUSTOM aggregation. This allows you to freely calculate a paint value and assign it to the built-in variable value in the Finalize code section.

Initialization code

In this section, you may specify the number of the first orbit element which should be processed. You can do this by assigning a value to the built-in variable start. Elements are numbered from 0. The default value is 1 which means skipping the initial orbit element.

Skipping the initial elements may be useful if your formula refers to previous elements (see the built-in Lights paint view definition for an example). It is also useful for MIN aggregation to avoid that there will be the same value at every point. That can happen for MIN(value) aggregation when the initial value is 0.

Simple definition paint modes always skip the initial value.

You may also declare your helper variables and give them initial values. You will need this for CUSTOM aggregation.

Iteration code

This is the most important section where a paint value is computed.

For the built-in aggregation methods (all but CUSTOM) you should at least calculate a value for the orbit element z and assign it to the built-in variable value.

For CUSTOM aggregation you should write a piece of code that calculates and aggregates a value using helper variables defined in the initialization code. The final paint value should be calculated in the Finalize code section.

Finalize code

You should define this section for CUSTOM aggregation. Write a piece of code that computes the final paint value and assigns it to the built-in variable value.

Use the built-in variable smooth to handle smoothing. When computing a paint mode for the fractal interior, smooth = 1.

You may also use this section for built-in aggregation to affect the final result (see how the built-in Foggy paint mode handles the Pattern intensity parameter).

Parameters

See the Custom parameters section.

Custom parameters

The app lets you define parameters for your custom fractal types and paint modes. Custom parameters will be presented in fractal or paint mode section of the scrollbar menu and you will be able to interactively change their values.


Example images of parametrized Mandelbrot Set zp+c using different values of the parameter p=2.05, p=2.15 and p=2.65 (from left to right respectively).

You may refer to the values of your custom parameters in MbLan expressions.

You may use parameters anywhere you want in a definition of a custom fractal type or paint mode. You may even use it for computing the bailout value and then observe how the change in value affects the image.

Parameters are presented on the bottom of a fractal type or paint mode definition (both advanced and simple).

Use the add button to create a parameter and define the following attributes:

Name A variable id that will be used to refer the parameter value in MbLan expressions.
Description A parameter description that will be displayed in the scrollbar menu and on the scrollbar. You may leave it empty and the parameter name will be used instead.
Type A parameter type: DOUBLE or INT.
Min value The minimal value of the parameter.
Max value The maximal value of the parameter.
Default value The default value of the parameter.
Scrollbar scale A scale type used by the scrollbar for this parameter: LINEAR or LOGARITHMIC. You can use LOGARITHMIC only if both min and max values are greater than zero.

Tap a parameter to edit it.

Tap a bin icon to delete a parameter.

You may create up to 10 parameters for one definition of fractal type or paint mode.

You may add new parameters to custom fractals and paint modes even if you have already used them for your favorite locations. The default values will be used for them when such location is opened. When you change min or max parameter value the values used in your saved location will be adjusted to fit the new range while opening.

Examples of using parameters can be found in the app's built-in fractal Generic Mandelbrot Set or the built-in paint mode Stripes.