This Little Image is Bigger Than A Universe | The Mandlebrot Set

Prepare to be blown away … No!

Really!!! Prepare to be blown away!

This image is a simple map of points created from a mathematical equation. What you are about to see is not a computer generated simulation. We are actually traveling through this image as we zoom in. The video is two hours long and is zooming in on just one point. You could sit and watch this all day and never get to the end. You could watch it all year and never get to the end. In fact, you will never get to the end! Those that know say the universe has boundaries. If you zoom in, you pass atoms, electrons, quarks and even the planck but they say there is a limit.

The Mandlebrot set … there is no end. This little image is a true universe!!!

The Mandlebrot Set

Wikipedia

The Mandelbrot set (/ˈmændəlbrɒt/) is the set of complex numbers c {displaystyle c}

for which the function f c ( z ) = z 2 + c {displaystyle f_{c}(z)=z^{2}+c}

does not diverge when iterated from z = 0 {displaystyle z=0}

, i.e., for which the sequence f c ( 0 ) {displaystyle f_{c}(0)}

, f c ( f c ( 0 ) ) {displaystyle f_{c}(f_{c}(0))}

, etc., remains bounded in absolute value. Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot, a pioneer of fractal geometry.

Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications, making the boundary of the Mandelbrot set a fractal curve. The “style” of this repeating detail depends on the region of the set being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point c , {displaystyle c,}

whether the sequence f c ( 0 ) , f c ( f c ( 0 ) ) , … {displaystyle f_{c}(0),f_{c}(f_{c}(0)),dotsc }

goes to infinity. Treating the real and imaginary parts of c {displaystyle c}

as image coordinates on the complex plane, pixels may then be coloured according to how soon the sequence | f c ( 0 ) | , | f c ( f c ( 0 ) ) | , … {displaystyle |f_{c}(0)|,|f_{c}(f_{c}(0))|,dotsc }

crosses an arbitrarily chosen threshold (the threshold has to be at least 2, but is otherwise arbitrary). If c {displaystyle c}

is held constant and the initial value of z {displaystyle z}

is varied instead, one obtains the corresponding Julia set for the point c {displaystyle c}

.

The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules. It is one of the best-known examples of mathematical visualization, mathematical beauty, and motif.