The Mandelbrot Set… what is THAT?
Back in 1985, my friend, Mark Lehman, and I began an exploration of something wonderful. Scientific American had published an article about the Mandelbrot Set and the emerging science of Chaos Theory. It was heady stuff! We read about a number set within the complex number plane which contained an infinite variety of images; images which were amazingly compelling. Seemingly, every image in the natural world could be found replicated within this thing... this Mandelbrot Set.
It’s interesting to note that it is only the computational power of computers that allows us to explore the mathematical underpinnings built into the entire universe… from life cycles to galaxies! A genuine understanding of the math is what steers mathematicians and scientists to see what they call “intelligent design”. Such a breathtaking mathematical ordering of every system in the universe could not be chance, but could only come from the hand of an awesome creator!
One of the most poetic descriptions of the Mandelbrot set is still one of the finest:
“The Mandelbrot set broods in silent complexity at the center of a vast two-dimensional sheet of numbers called the complex plane. When a certain operation is applied repeatedly to the numbers, the ones outside the set flee to infinity. The numbers inside remain to drift or dance about. Close to the boundary minutely choreographed wanderings mark the onset of the instability. Here is an infinite regress of detail that astonishes us with its variety, its complexity and its strange beauty.”
- A. K. Dewdney, Scientific American, August 1985
To try and put the mathematics in laymen’s terms, let’s consider first that the boundary of the Mandelbrot set is an example of a fractal. A fractal is a mathematical object that is self-similar at every level of magnification. Nowhere will you find a fractal with more intricacy and complexity than the Mandelbrot set. And somehow, this infinite complexity is the product of a ridiculously simple formula. The representation of the Mandelbrot set at first appears to be nothing but an ugly bug with warts. But when you zoom in on its edges, incredibly intricate patterns begin to emerge. Spirals, jellyfish, bow ties, and many other beautiful, bizarre objects abound in infinite numbers on the edge of the Mandelbrot set. And everywhere you look, at every level of magnification, miniature versions of the Mandelbrot set keep popping up.
Here’s a quick trip into a tiny segment of the infinite beauty of the Mandelbrot Set:
Now, as promised, here is a neat little examination of numbers. Some of you will pull out your calculator to check on these computations (I know I did), but it all works out. This is really cool and fun. Consider for a moment…
The Beauty of Mathematics!
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
Brilliant, isn't it?
And look at this symmetry:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
Mind Boggling...
Now, take a look at this...
What does it mean to give MORE than 100%?
From a strictly mathematical viewpoint:
What Equals 100%?
Ever wonder about those people who say they
are giving more than 100%?
We have all been in situations where someone wants you to
GIVE OVER 100%...
How about ACHIEVING 101%?
What equals 100% in life?
Here's a little mathematical formula that might help
answer these questions:
If:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Then:
H-A-R-D-W-O-R-K
is
8+1+18+4+23+15+18+11 = 98%
And:
K-N-O-W-L-E-D-G-E
K-N-O-W-L-E-D-G-E
is
11+14+15+23+12+5+4+7+ 5 = 96%
But…
A-T-T-I-T-U-D-E
is
1+20+20+9+20+21+4+5 = 100%
THEN, look how far the love of God will take you:
L-O-V-E-O-F-G-O-D
is
12+15+22+5+15+6+7+15+4 = 101%
Therefore, one can conclude with mathematical certainty that:
While Hard Work and Knowledge will get you close,
And Attitude will get you there,
It’s the Love of God that will put you over the top!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
With just a few seconds of tweaking, I can use the same trick to produce the answer to the question:
How can we achieve salvation?
I-N-C-H-R-I-S-T
and that is
9+14+3+8+18+9+19+20 = 100%
Yes, we do achieve salvation in Christ, but Jesus commands us to love one another… not trick one another! The bit about hard work, knowledge, attitude, and the love of God is fun, but it is a trick of man… not to be confused with the awesome building blocks of God’s incredible creation… that we dimly perceive as mathematics and science.
This week, as you worship and pray, open your eyes to the awesome wonder and beauty of God’s creation… of which you are a most beloved part. Can you sense the world spinning in its orbit around the sun? Think about our solar system being a speck in the rotating spiral arm of a galaxy. It is just as impossible for you to detect our galaxy’s flight through the universe, as it would be for you to detect the orbit of a single electron about an atom somewhere in your body. We are fearfully and wonderfully made!
In that infinite vastness… whether out to the unimaginable scope of the universe, or inward to the strange atomic forces that are just as unimaginable… in all of that creation God loves you. In all of that infinity, God knows just where you are. Open up your heart, let Christ in, and begin a real relationship with the creator and sustainer of the universe!
Your brother in Christ,
Dave
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