Transformed Shape Minimum

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Alternate Mapping: Transformed Shape Minimum

The Fractal Science Kit fractal generator Alternate Mapping Transformed Shape Minimum applies a transformation to each orbit point and the point with the minimum magnitude is used to determine the resulting value. In addition to the base transformation, a shape transformation is also applied.

See also:

The Transformed Shape Minimum properties pages are:

The Properties page supports several properties to control the results.

Fractal Science Kit: Transformed Shape Minimum

General Options

Before the orbit point P is passed to Transformed Value Minimum for processing, it is transformed by Transformation. When a point P is transformed, it is understood that P is passed through the transformation and the resulting transformed point placed back in P.

Next, a shape transformation based on properties defined in the Shape Options section (see below) is applied. This injects a simple orbit trap like quality into the value based on the selected shape transformation properties.

Next, Variation is applied.

Variation is one of:

  • None
  • Angular Wave
  • Angular Bounce
  • Radial Wave
  • Radial 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.

Finally, the magnitude is used to determine which point P is kept as the minimum across all the points in the orbit.

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

The alternate point's Angle is set to the angle of P based on the Angle Options (see below).

The alternate point's Index is set to the dwell value associated with P.

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.

Angle Options

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
  • Z Prior to Transformation

Origin is the point 0+0i. Z Prior to Transformation is the original orbit point value prior to applying the 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.


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