Alternate Mapping: Average Value
The Fractal Science Kit fractal generator Alternate Mapping Average Value returns the average value over all points P in each orbit.
The Average Value properties pages are:
The Properties page supports several properties to control the results.
The Value property controls which values to process. Value is one of:
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. 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 and the Previous Point is the previous Triangle Metric point.
The alternate point's Value is set to the average value. Uncheck Compute Value to skip the value calculation. Quadratic Value and Angle Factor can be used to modify the calculation. Check Quadratic Value to compute the quadratic mean rather than the arithmetic mean. Angle Factor is an integer value between 0 and 16. Setting Angle Factor to a value other than 0 perturbs the value based on the angle of the orbit point.
If Value is Orbit Transformation or Triangle Metric, the Type property is enabled and can be set to Type 1 or Type 2. Type controls the type of the average value calculation. Type 1 averages the value. Type 2 averages the product of the Value and the Magnitude.
The alternate point's Angle is set to the average angle of P. Uncheck Compute Angle to skip the angle calculation. Quadratic Angle, Angle Power, and Angle Vertex 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.
The angle is defined by the vector from the Angle Vertex to P. Angle Vertex is one of:
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. All points are based on the selected Value. For example, if Value is Triangle Metric, the Previous Point is the previous Triangle Metric point.
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.
The alternate point's Index is set to the quadrant (0 to 3) of the Angle and is used to improve the visible results of Solid Guessing.
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.
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