Fractal Generator: The Mandelbrot Set....NOT Your Average Blog!
Video link/s to the famous Mandelbrot Set - To Some of the Highest Levels of Detail Ever Recorded! (i.e the most Iterations)...The Mandelbrot Set was discovered (mathematically) by Benoit Mandelbrot, (in 1980).
To Infinity, and Beyond? (At the Microscopic Level)?
This would seem to suggest Infinity is possible in the reverse direction (Think Zeno's Paradox). It is all a matter of scale. To think in this way; is to understand how the Big Bang could have come from an Infinitely Small Singularity. In fact, all of the Cosmological Evidence (background radiation) would seem to point toward the veracity of this statement.......
To Infinity, and Beyond? (At the Macroscopic Level)?
Consider this, now, from the Reverse Point of View: Since the MS is Infinite in one direction; then why not the other way around? Likewise, this would seem to suggest that the Universe is Infinite at Vast Scales; which the human mind cannot process; and indeed fits the Mathematical Definition of Genuine Infinity....(there are various interpretations of this).......
Here the Argand Plane is used:
The x-axis (horizontal) represents the Real Numbers;
(as in a Cartesian standard graph)
The y-axis (vertical) represents the Imaginary Numbers;
(designated the iy axis);
where i = (-1)^1/2 = {the square root of (-1)}
Therefore, any Complex Number z can be written in the form:
z = a + ib
For any point (a,ib) on the Complex Plane.
The Real part of the Complex Number z is written:
Re(z) = a
The Imaginary part of the Complex Number z is written:
Im(z) = b
The iterative function f(z) For the Mandelbrot Set is:
f(z) = z^2 + C (for any complex constant C)
On the Argand plane (x, iy) axis.
(Start with z = 0)
Fractals at ANY level of magnification will produce self-similar but NOT Identical Patterns (generated by the information contained in the Original Set)....
Everything in Nature is Fractal; (The classic example would be a snowflake) - they are all indeed different, yet superficially the same; due to their self-similarity. Other examples would include leaves on a tree, and forks of lightning....
The Universe itself, is Fractal/Chaotic
This is why (mathematically) these Fractal Sets are very significant and important to study...
The Mandelbrot Set is probably the most famous fractal set; although there are many others (depending on the mathematical parameters chosen, and, of course, the initial function)...
These are the Link/s (below):
There are higher levels of Magnification (Iterations) available, like this one:
The final image, here, is Magnified to 10^4004 (10 to the power of 4004). That is to say, a phenominally Large Number.
Or in other words, the number 10, with 4004 zeros after it! - (or 400,000 Iterations).
Only to get to a "typical" MS motif at the end......(Completely Mind Blowing!)
And two 3D ones for Enthusiasts:
(These are usually based on a 4D form of Complex Numbers called Quaternions)
I really recommend this one..
And...
The math is further explained, here (for those interested in more detail)...
Btw, I'm Not trying to show off here, I just find the Mandelbrot Set (and Fractals, in general) to be F..king Amazing!.......
***TRIGGER WARNING**** Use Extreme Caution if you have Epilepsy, or are otherwise susceptible.....
Watch and be amazed
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