# Minimum Value # Alternate Mapping: Minimum Value

The Fractal Science Kit fractal generator Alternate Mapping Minimum Value returns data for the point P with the minimum value in each orbit.

The Minimum Value properties pages are:

The Shape Transformation page defines a transformation applied to each value (see Apply Shape below).

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. Both P and the associated value are based on the Value property. For example, if Value is Triangle Metric, P is the Triangle Metric point with the minimum Triangle Metric value.

The alternate point's Value is set to the minimum value.

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.

The alternate point's Angle is set to the angle of P based on the Angle Vertex property. The angle is defined by the vector from the Angle Vertex to P. Angle Vertex is one of:

• Origin
• Previous Point
• Second Previous Point

Origin is the point 0+0i. Previous Point is the point just before P in the orbit. Second Previous Point is the point just before the Previous Point in the orbit. Like P, the Previous Point and the Second Previous Point are based on the selected Value. For example, if Value is Triangle Metric, P is the Triangle Metric point with the minimum Triangle Metric value and the Previous Point is the previous Triangle Metric point.

If Smooth Angle is checked, the alternate point's Angle is set to the smoothed angle over the entire orbit rather than the angle at P. The smoothed angle is the weighted average angle, where the weight is based on the point's value relative to the minimum value. If Smooth Angle is checked, Quadratic Angle and Angle Power can be used to modify the calculation. Check Quadratic Angle to compute the quadratic mean rather than the arithmetic mean. Angle Power is a real value greater than 0. Setting Angle Power to a value other than 1 perturbs the angle based on the given power.

Check Rotate 180 to rotate all angles 180 degrees prior to processing. This is useful if most of the angles cluster around +/- 180 degrees.

Check As Value to set the alternate point's Value to the angle rather than the point's value as is normally the case. This is useful if you don't need the value and you want better control over the normalization processing applied to the angle.

Check Apply Shape to apply the Shape Transformation to each value. This injects a simple orbit trap like quality into the value based on the shape defined by the Shape Transformation.

# 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.