$TRANGE WORLD

You were visited by the magic kitten of rest. Reblog to have a good night’s sleep.

I’m proud of him

RED CENTURY

…Dan McPharlin…Future Past / Past Future…

Unveiling the Mandelbrot Set. Back in the 1970s and 1980s, mathematicians working in an area called dynamical systems made use of the ever-advancing computing power to draw computer images of the objects they were working on. What they saw blew their minds: fractal-like structures whose beauty and complexity is only rivalled by Nature itself. At the heart of them lay the Mandelbrot set, which today has achieved fame even outside the field of dynamics.  The Mandelbrot set is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers. The Mandelbrot set is an incredible object that equals infinity. It’s really amazing that the simple iterated equation Z = Z^2 + C can produce such beautiful works of mathematical art.

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line… Nature exhibits not simply a higher degree but an altogether different level of complexity. The number of distinct scales of length of natural patterns is for all practical purposes infinite. The existence of these patterns challenges us to study these forms that [traditional plane geometry] leaves aside as being ‘formless’.” – Benoît Mandelbrot

If you want to know more about constructible polygons this is a good place to start: https://en.wikipedia.org/wiki/Constructible_polygon

Stare at the middle. It looks like it is turning, but is it?

…Dan McPharlin…Future Past / Past Future…

50 YEARS AGO TODAY: Beautiful views of the Earth captured from the orbiting Gemini 12 spacecraft, docked with the Agena target vehicle, November 12, 1966. (NASA/ASU)

Lithograph, 32 x 38 cm

M.C. Escher, Phosphorescent Sea, 1933.