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.
See also:
The Minimum Value properties pages are:
- Shape Transformation
- Properties
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.
The Value property controls which values to consider. 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.
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.
The alternate point's Index is set to the dwell value associated with P.
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 looking for the minimum value. 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.