Atlas of the Mandelbrot set

M. Romera

Instituto de Física Aplicada
Consejo Superior de Investigaciones Científicas
Serrano 144, 28006 Madrid, Spain

When an atlas is used, a length unit to measure objets sizes and distances between points is needed. The width of the main cardioid of the Mandelbrot set, i.e. the distance between the cusp of the main cardioid and the point where the period-2 disk is tangent to the main cardioid, is equal to unity. I name this distance as 1 M, where M is the length unit "Mandelbrot". Thus, the period-2 disk centered in the point (-1, 0) has a diameter of 0.5 M.

The Atlas of the Mandelbrot set has 13 x 4 = 52 pages. Every one of these pages, when it is printed, has a size of A4 (210 x 297 mm) or Letter (8.5" x 11") and covers a surface of
0.2 M x 0.3 M. Only 27 of these pages belong to the boundary of the set; the remaining 25 pages have no information. The atlas resolution is 0.0001 M.

If you want to obtain a hard copy of the Atlas, it can be useful to test the printing process. For this, you can use Test.gif. This image is 2272 pixels width and 3104 pixels height, and it must to be printed with a resolution of 300 pixels per inch (if the printer resolution in your drawing editor is 600 pixels per inch you must change it into 300). So, Test.gif has a total size of
192.4 mm width and 262.8 mm height. When a hard copy of Test.gif is obtained you have to verify that the distances 6 2/3" = 169.3 mm and 10" = 254 mm on the paper are OK.



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Last update: 28 July, 1999 (JNE)