Order In Chaos: How The Mandelbrot Set & Fractal Geometry Help Unlock the Secrets of The Entire Universe! (Mandelbrot Set, Fractal Geometry) by Tim Clearbrook & Clarence T. Rivers

Author:Tim Clearbrook & Clarence T. Rivers [Clearbrook, Tim]
Language: eng
Format: azw3
Published: 2014-01-14T05:00:00+00:00

Figure 5: Selected Thumbnails of Mandelbrot Views

Chapter 5: Unlocking the Secrets of the Universe

It was almost impossible, but the Mandelbrot set was able to open the doors of one of the most intriguing mysteries on earth: what the universe is actually like. In the spring of 1980, Mandelbrot was astounded when vague patterns started to appear on computer printouts that reflected the writings of Keat’s poetry:

Charmed magic casements, opening on the foam

Of perilous seas, in faery lands forlorn. (Clarke 2010, 30)

Brought by the prospect of the advanced technology, mathematicians began to ponder what shape the universe would be if they assigned numbers using the equation in the Mandelbrot set. When they used z= 1 to calculate any given point in any area, the result turned out to be some kind of map with a spiral object, where inside the plane, the numbers are trapped until it reaches zero, and outside the plane they are being squared to infinity. The object that lies inside the map would have a frontier in the center of the circle enclosing it, and the circle would be a continuous line that has no thickness. This happens when you choose a specific point around us and then calculate z to be graphed in the computer.

Now, mathematicians tried to find out what it would be like if they were to calculate in large scales towards infinity so that the shape of the universe would be revealed. The result was a continuous boundary line that had no thickness, but unlike the usual, there were no holes found in it simply because the barrier was impenetrable, with nothing that separated the z < 1 and the z > 1. In the usual course, the line would shift to the left of the map, which constitutes numbers from +1 to -1 in the x-axis. However, when calculating towards infinity, the line only gets until 0.25 somewhere on the right of the horizontal axis, and then bulges above and below the axis line to beyond 0.4.[xvii] Arthur Clarke tried to explain this furthermore when he stated,

On the left-hand side, the map stretches to about -1.4, and then it sprouts a peculiar spike—or antenna—which reaches out to exactly -2.0. As far as the M-set is concerned, there is nothing beyond this point; it is the edge of the Universe. (Clarke 2010, 32)

They called this point the “Utter West”, wherein the line stays put if c = -2. It neither decreases to zero nor increases to infinity.[xviii] However, when c = -2.0000001, it would go on towards infinity, and the line stretches as it passes towards the planets outward beyond the solar system.[xix] In this case, the frontier would be fuzzy, unless it would be “zoomed” and incredible colors would be seen in the map. Mandelbrot tried to describe this unimaginable discovery when he tried to find in the dictionary words that would suit the images that are reflected in the graphical representations of the Mandelbrot set. He used the words foams, sponges, dusts, webs, nets, and curds to describe them; yet the beauty remains indescribable.

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