In mathematics the Mandelbrot set is a set of points in the complex plane, the boundary of which forms a fractal.
You can zoom in on any portion of a fractal to any degree and it becomes infinitely complex indefinitely.
Here is a zoomed out picture:
http://farm4.static.flickr.com/3232/2767692001_ac8b7a91ea.jpg
And a video animation if you are interested:
http://www.youtube.com/watch?v=G0nmVUU_7IQ
An extremely simple equation is all that it takes to describe the infinite complexity of this fractal.
Zn+1 = Zn² + C (lowercase letters indicate subscript)
Which just means the next Z is equal to the Z before it squared plus C.
On a complex plane, you would pick any point on the complex plane (C) and start the equation with Z=0 and continue solving the equation.
So you would say 0² + the complex number C = Zn+1, and then you would substitute Zn=1 for Z and repeat. When the solution for the point does not reach infinity, it is colored black and is considered to be a part of the Mandelbrot set. The other colors are chosen based on, as you iterate on the formula, how fast the solution reaches infinity.
Taking the linked picture, which designer is more intelligent, the designer who paints the picture in all of its complexity from scratch, or the designer who creates an extremely simple and universal equation that creates the infinitely complex design.
Please explain why.
There is no correct answer, but the most well supported answer will receive BA.
NOTE: This is a repost.
@Objection
This was not meant to address specified complexity, but infinite complexity. The purpose was already defined (replicating an infinitely complex image). The being in question is either more intelligent by painting this image from scratch, or creating it via an equation (or set of equations).
@aggymemnon
I am assuming a designer as this question is directed at proponents of intelligent design. I accept the fact of evolution and that simple laws can create great specified complexity.
@Publius, I have come to the same conclusion; now, if you could please give an definitive answer...
Edit: You beg the question of how a designer would make such an infinitely complex object "from scratch" without describing it mathematically. If the designer's goal is to make such an object, and there were any less efficient a way of doing it than a mathematical description, then that method would reflect a lesser intelligence if and only if the mathematical method were somehow beyond the designer's capabilities. Otherwise, it reflects a choice based on the designer's goals, not its intelligence.
@Objection, "from scratch" is essentially via magic (however that works). And the only goal set is to replicate the object. I am asking if a more intelligent designer would replicate it through magic, or if he/she would just set up an equation to replicate it. This is precisely why there is no correct answer, it is based on *your* opinion of what would be a more intelligent decision, given only one goal. In other words, what choice do you deem more intelligent?
And, yes, this is based on whatever you define as intelligence.
You can zoom in on any portion of a fractal to any degree and it becomes infinitely complex indefinitely.
Here is a zoomed out picture:
http://farm4.static.flickr.com/3232/2767692001_ac8b7a91ea.jpg
And a video animation if you are interested:
http://www.youtube.com/watch?v=G0nmVUU_7IQ
An extremely simple equation is all that it takes to describe the infinite complexity of this fractal.
Zn+1 = Zn² + C (lowercase letters indicate subscript)
Which just means the next Z is equal to the Z before it squared plus C.
On a complex plane, you would pick any point on the complex plane (C) and start the equation with Z=0 and continue solving the equation.
So you would say 0² + the complex number C = Zn+1, and then you would substitute Zn=1 for Z and repeat. When the solution for the point does not reach infinity, it is colored black and is considered to be a part of the Mandelbrot set. The other colors are chosen based on, as you iterate on the formula, how fast the solution reaches infinity.
Taking the linked picture, which designer is more intelligent, the designer who paints the picture in all of its complexity from scratch, or the designer who creates an extremely simple and universal equation that creates the infinitely complex design.
Please explain why.
There is no correct answer, but the most well supported answer will receive BA.
NOTE: This is a repost.
@Objection
This was not meant to address specified complexity, but infinite complexity. The purpose was already defined (replicating an infinitely complex image). The being in question is either more intelligent by painting this image from scratch, or creating it via an equation (or set of equations).
@aggymemnon
I am assuming a designer as this question is directed at proponents of intelligent design. I accept the fact of evolution and that simple laws can create great specified complexity.
@Publius, I have come to the same conclusion; now, if you could please give an definitive answer...
Edit: You beg the question of how a designer would make such an infinitely complex object "from scratch" without describing it mathematically. If the designer's goal is to make such an object, and there were any less efficient a way of doing it than a mathematical description, then that method would reflect a lesser intelligence if and only if the mathematical method were somehow beyond the designer's capabilities. Otherwise, it reflects a choice based on the designer's goals, not its intelligence.
@Objection, "from scratch" is essentially via magic (however that works). And the only goal set is to replicate the object. I am asking if a more intelligent designer would replicate it through magic, or if he/she would just set up an equation to replicate it. This is precisely why there is no correct answer, it is based on *your* opinion of what would be a more intelligent decision, given only one goal. In other words, what choice do you deem more intelligent?
And, yes, this is based on whatever you define as intelligence.