mandelbrot_distance.cpp File Reference

This program draws a mandelbrot set using the "distance". More...

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Detailed Description

This program draws a mandelbrot set using the "distance".

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

Copyright

Copyright (c) 1988-2022, Mitchell Jay Richling https://www.mitchr.me All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Details

The normal Mandelbrot raster scan iteration fails to illustrate the thin filaments projecting off the Mandelbrot set – because the complex number at the center of the pixel misses the set, and thus the entire rectangular region of the complex plane covered by the pixel is marked as "escaped". In order to provide some graphical representation of these filaments, we can use a the Milnor and Thurston distance estimator as presented in 'The Science of Fractal Images' to draw pixels that have a center "close" to the Mandelbrot set. This program uses a simple color scheme to label points as described in the comment for the pixelStateEnum enumeration. All of the drawing code is confined to a switch statement at the end of the x loop to make it easy to play around with various color schemes.

Reference: Peitgen, Heinz-Otto and Saupe, Dietmar; 1988; The Science of Fractal Images; ISBN: 0-387-96608-0; pp 192-196

Definition in file mandelbrot_distance.cpp.