Robert P. Munafo, 2002 Apr 18.
Refers to the act of multiplying complex numbers by themselves, and the analogous transformation seen in images such as Julia sets, that are generated by functions that have a quadratic behavior.
When you square a complex number, you can look at the operation two ways. One way is like this:
C2 = C × C = (a+bi) × (a+bi) = a2 - b2 - 2abi
You can also "square" any set of points in a 2-d space, such as an image or a part of an image. In this case you need to specify a center from which the angles and radii are to be measured. The squaring operation transforms the image in a way that makes it larger, stretches the outer parts more than the inner parts, and (if the original image completely surrounds the center point) wraps the image around twice, overlapping itself everywhere so that there are two parts of the squared image in any one area of the plane.
The opposite operation is the square root mapping
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.
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