Brooks-Matelski Set
2023 Jun 21.
The interior of the Mandelbrot Set was imaged by Brooks and Matelski a year or two before Mandelbrot himself saw it, and so it is sometimes referred to as the "Brooks-Matelski Set".
(-.07,.96) * **** ****** ***** * ********* *** **************** ******************** ** ************************* **************************** ******************************* ****************************** * ***** ******************************** ********** ******************************** ************ ******************************* ** ************* ****************************** 1 *************************************************************** (-,0) (-2,0) ** ************* ****************************** 4 ************ ******************************* ********** ******************************** * ***** ******************************** ****************************** ******************************* **************************** ************************* ******************** ** *** **************** * ********* ***** ****** **** * 2 The set of C's such that f(z)=z +C has a stable periodic orbit. The Mandelbrot set, as imaged by Brooks and Matelski
(0,1.2) * *** **** * **** * ******** **** * *** ******* *********** **** ********** ************* * ****** ****** * * ** * ************ **** *************** ******************** ********************* ******************************************** ******** ************************************ *** * * *********************************** * ***** ***************************** *** ** ** **** **** ********************************* ** *********************************** ******************************** *************************** * ** ******************************* **************************** ********** *************** **** * ************************ ** * *********************** ************************* *********************** * ** ************************ * **** *************** ********** **************************** ******************************* **** *************************** ******************************** ********************************** ** ******************************** **** **** ** ** *** ***************************** ***** * *********************************** * * *** ************************************ ******** ******************************************** ********************* ******************** *************** **** ************ * ** * * ****** ****** * ************* ********** **** *********** ******** *** * **** ********* * **** * **** *** * (0,-1.2) 2 The set E for f(z) = z +C with C=.1+.6i A Julia set as imaged by Brooks and Matelski
Both images, in classic ASCII art style, are from their 1978 paper (see reference below).
See History.
Robert Brooks and J. Peter Matelski, The dynamics of 2-generator subgroups of PSL(2,C), Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, Princeton University Press, 1980. (0-691-08264-2/80/000065-07).
revisions: 20080220 oldest on record; 20100129 add link to reference; 20230621 labels and captions
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.
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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2023 Jun 21.
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