Exploring the Mandelbrot Set
Eamonn O'Brien-Strain
This site is a showcase for Mandelbrot set images generated by the almondbread software. For more background on my fascination with this set and the development of the software see Finding Mandelbrot images to use as video conference background
Click on any image to view a full-resolution version, suitable for example as a video conferencing background.
What you are looking at
These are images of the space of complex numbers.
The black area is the Mandelbrot set itself, which are the values of the complex number c such that if you repeatedly iterate z ← z² + c starting at z=0 the value of |z| stays less than 2. The colored areas surrounding the black of the Mandelbrot set are values of c for which z eventually goes to infinity, with the colors indicating how many iterations until |z|>2
You will also notice a subtle shading which seems to show relief. This is done by considering that the colored bands to be contours on a map and shading it accordingly to show the slope. For a detailed discussion of the algorithm see Hill-Shading the Mandelbrot Set
Out of these simple mathematical operations we get these incredibly complex and fascinating images.
See also color renderings.
Images
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If the Mandelbot set were the size of the Earth this image would be 22 thousand kilometers (36 thousand miles) wide.
-0.756488542 +i0.066764459
At 8,000,000× magnification. If the Mandelbot set were the size of the Earth this image would be 66 cm (26 inches) wide.
-1.953256636604 +i0.000001341718
At 8,000,000× magnification. If the Mandelbot set were the size of the Earth this image would be 0.6 millimetres wide.
0.350896626980250 -i0.421429523450479
At 9,000,000,000× (nine billion) magnification. If the Mandelbot set were the size of the Earth this image would be 3 μm wide.
-0.103752576387449 +i0.9250308323744141
At 35,000,000,000,000× (35 trillion) magnification. If the Mandelbot set were the size of the Earth this image would be 160 nm wide.
-1.041538154494949 +i0.266417845161627
At 35,000,000,000,000× (35 trillion) magnification. If the Mandelbot set were the size of the Earth this image would be 160 nm wide.
-0.5622024519151031 +i0.6428171823242691
At 20,000,000,000,000× (20 trillion) magnification. If the Mandelbot set were the size of the Earth this image would be 28 nm wide.
-1.76832484808631 +i0.0514179497525385
At 300,000,000,000,000× (300 trillion) magnification. If the Mandelbot set were the size of the Earth this image would be 20 nm wide.
-1.041538154494943 +i0.2664178451616198
At 300,000,000,000,000× (300 trillion) magnification. If the Mandelbot set were the size of the Earth this image would be 20 nm wide.
-1.4237083134223119 +i0.0000002787841555
At 56,000,000,000,000× (56 trillion) magnification. If the Mandelbot set were the size of the Earth this image would be 10 nm wide.
-0.24482766477704102 +i0.8132688560198666
At 1,000,000,000,000,000× (1 quadrillion) magnification. If the Mandelbot set were the size of the Earth this image would be 50 Å wide.
-1.3551734861174762 +i0.04053190336270575
Another image ar 1,000,000,000,000,000× (1 quadrillion) magnification. If the Mandelbot set were the size of the Earth this image would be 50 Å wide.
mandelbrot.dev website by Eamonn O'Brien-Strain is licensed under CC BY-NC-ND 4.0 
