Shape Transformation 

Shape Transformation Properties PageThe Fractal Science Kit fractal generator Shape Transformation page defines a transformation based on a given shape or a blend of 2 shapes. To transform a point, the input point's angular measure relative to the origin is calculated and a delta value is computed by finding the shape's radial measure for the given angle. The delta is applied to the original point to obtain the transformed value. See also: Shape Transformation
The Type field in the Shape Transformation section of the page defines how the shape is defined and can be one of the following values:
If Type is Shape 1 then only the Shape 1 section is enabled and the resulting transformation is based solely on the shape defined in that section. Otherwise, both the Shape 1 and Shape 2 sections are enabled and the resulting transformation is based on a blend of the 2 shapes given by Type. Minimum and Maximum use the shape with the minimum/maximum radial value for a given angle. Sum, Difference, Product, Quotient, and Power, apply the indicated operation to the 2 radial values for a given angle. The various means compute the mean of the 2 radial values for a given angle using the named method. The angle blends divide the complex plane into N sectors, where N is given in the name, and blend the shapes such that Shape 1 is dominant in even sectors and Shape 2 is dominant in odd sectors. Similarly, the dwell blends arrange that Shape 1 and Shape 2 oscillate over a period of N dwells. Shape 1 / Shape 2
The Shape 1 and Shape 2 sections contain 4 fields: Type, R, N, and S. Each section defines the associated shape used in the transformation blend. Type is the type of shape, R controls the shape's size and equates to the shape's radius unless stated otherwise, N is an integer argument specific to the shape, and S is a floating point argument specific to the shape. R, N, and/or S are enabled as required based on the shape's type. The text of Type contains details as to how R, N, and S are interpreted by the given type. The following list gives the possible values for each shape's Type:

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