# Alternate Mapping: Minimum Shape

The Fractal Science Kit fractal generator Alternate Mapping Minimum Shape returns data for the point P with the minimum value in each orbit. A shape transformation is applied to each orbit point at the beginning of each iteration.

The Minimum Shape properties pages are:

• Properties

The Properties page supports several properties to control the results.

# General Options

The Value property controls which values to process. Value is one of:

• Magnitude
• Orbit Transformation
• Triangle Metric

Magnitude is given by the Magnitude property on the Mandelbrot / Julia / Newton page. Orbit Transformation is defined by the Orbit Transformation page. Triangle Metric is defined by the Triangle Metric page. The alternate point's Value is set to the minimum value. The alternate point's Index is set to an index based on Index Map. Angle is the angle associated with the minimum point.

If Delta Value is checked, the point used in the calculation is relative to the previous orbit point rather than the origin.

Variation is one of:

• None
• Angular Wave
• Angular Bounce
• Horizontal Wave
• Horizontal Bounce
• Vertical Wave
• Vertical Bounce
• XY Wave
• XY Bounce

Variation sets the wave/bounce transformation applied to the value. The amplitude/frequency of the wave/bounce are given by the Amplitude and Frequency properties. Both properties can be positive or negative but not 0.

Index Map controls the value of the alternate point's Index.

# Shape Options

The Shape Options section allows you to control the shape transformation applied to each orbit point at the beginning of each iteration.

Shape defines the shape associated with the shape transformation applied to the value.

If Solid is checked, the shape transformation is based on a solid shape. Otherwise, the transformation is based on the border of the shape.

Radius defines the radius of the shape and is only important if the shape is not solid.

# Orbit Generation

The Orbit Generation section defines 3 properties: Min Dwell, Max Dwell, and Mod Dwell. These values control the set of orbit points that are considered when processing the orbit. Min Dwell is the 1st dwell to check. Max Dwell is the last dwell to check. Mod Dwell - 1 is the number of dwells to skip between checks. That is, a dwell is processed if the dwell is between MinDwell and MaxDwell inclusive, and (dwell - MinDwell) % ModDwell = 0.