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Fractals

Alkatran

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I've always known about fractals and even looked at programs that let you zoom in before. But I never appreciated them until I wrote a program to make them myself. It's AMAZING that something so complicated can come out of such a simple program!

I spent way too much time just looking around the mandlebrot set.

I also found out you can make even weirder ones by alternating between two functions.
 

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Alkatran said:
I've always known about fractals and even looked at programs that let you zoom in before. But I never appreciated them until I wrote a program to make them myself. It's AMAZING that something so complicated can come out of such a simple program!

I spent way too much time just looking around the mandlebrot set.

I also found out you can make even weirder ones by alternating between two functions.
Click to expand...

Yup!

A couple of years ago in Oregon I saw Mandelbrot give a presentation to the general public on fractals. It was really neat!
 
My housemate has a multi-processor demo for his 12 node cluster that calculates up to 10000 iterations - it's pretty sweet :D
 
Alkatran said:
Wow, they're talking about taking days to generate them. I stuck with a simple 255 maximum iterations, haha.
Click to expand...
They may have a mode now that permits high "magnification" that requires a lot of time, but I assure you that it has been very fast in the past.

It is a lot like using a microscope - zoom in, zoom out - gorgeous, gorgeous images.
 
Alkatran said:
I've always known about fractals and even looked at programs that let you zoom in before....
Click to expand...
I was led here after doing a search for Mandelbrot Set in this forum, after watching an AMAZING program on TV yesterday called "The colors of Infinity" (Gordon Films 1995). It had wonderful visuals, Pink Floyd music. and lots of clever mathematicians.
What really stood out for me was near the end, when someone pointed out how some of the patterns produced by computers using a formula which I think was z=z2+c (it's meant to be z squared, and the = sign is meant to be one of those signs with arrows going left and right) were similar to those that the psychologist Carl Jung had seen his subjects draw, and had lead him to formulate his theory of a "collective unconscious".
This was one of the best programs I have seen to convince me that science is beginning to understand consciousness, or, to some people, "the mind of God".
 
Time is no longer a concern for Mandelbrot plots, unless you go into ridiculously high numbers of iterations, but there is really no need to. Those plots that took days were on ye olde 8 mHz computers. Modern gigaherz boxes do the same in minutes, or even seconds. I wrote a couple of Mandelbrot plotters myself.

http://www.hans-egebo.dk/files/mandel.zip
http://www.hans-egebo.dk/files/pattern.zip

The graphics is now outdated. I also recommend Fractint.

Hans
 
Not only is Fractint a wonderful program to use, it's also the manifestation of an awesome array of smarts. So much talent and ingenuity poured into one program. Shame it can't be made open source at this late date but that's how it goes with so long-lived a project.
 
Aquila said:
I was led here after doing a search for Mandelbrot Set in this forum, after watching an AMAZING program on TV yesterday called "The colors of Infinity" (Gordon Films 1995). It had wonderful visuals, Pink Floyd music. and lots of clever mathematicians.
What really stood out for me was near the end, when someone pointed out how some of the patterns produced by computers using a formula which I think was z=z2+c (it's meant to be z squared, and the = sign is meant to be one of those signs with arrows going left and right) were similar to those that the psychologist Carl Jung had seen his subjects draw, and had lead him to formulate his theory of a "collective unconscious".
This was one of the best programs I have seen to convince me that science is beginning to understand consciousness, or, to some people, "the mind of God".
Click to expand...

First of all, "<=>" means "equivalent" which is ..er equivalent to saying equal or using "=" for the most part. Secondly, the Mandelbrot set has nothing to do with the mind of God. It's just what (amazingly) happens when you draw out the line for z <=> z^2+c. There are lots of other fractals.

I also have no idea why people drawing things that look similar would mean a collective unconscious...
 
I've been interested in fractals since I first learned about them about 1980. In the mid-80's while I was in college, my roommate found a copy of Scientific American that gave the basic algorithms for the Mandelbrot set. He wrote a short Fortran program and we ran it on the university's mainframe system. It took about 8 hours to create a simple black-on-white Mandelbrot set. The university would only let him run the program at night because it bogged down the system so much.

My favorite fractal program is Ultra Fractal. There are hundreds of formulas and coloring options to use and build upon. You can have multiple layers with various blend modes, like Photoshop. They have a free demo you can play with. Below are a few pics that I've done.

Another cool fractal program is Apophysis.

fract2.jpg


fract1.jpg


fract3.jpg


Steve S.
 
steve s said:
I've been interested in fractals since I first learned about them about 1980. In the mid-80's while I was in college, my roommate found a copy of Scientific American that gave the basic algorithms for the Mandelbrot set. He wrote a short Fortran program and we ran it on the university's mainframe system. It took about 8 hours to create a simple black-on-white Mandelbrot set. The university would only let him run the program at night because it bogged down the system so much.

My favorite fractal program is Ultra Fractal. There are hundreds of formulas and coloring options to use and build upon. You can have multiple layers with various blend modes, like Photoshop. They have a free demo you can play with. Below are a few pics that I've done.
Another cool fractal program is Apophysis.


http://www.photochimps.com/gallery/data/604/fract3.jpg

Steve S.
Click to expand...
Ahh, I love the 3D Mandelbrot. I have worked a lot on that type of rendition, but I could never get it right.

Hans
 
Alkatran said:
I also have no idea why people drawing things that look similar would mean a collective unconscious...
Click to expand...
The makers of this film said that some people had suggested that there might be a collective unconsious, (which is presumably where math comes from) because these patterns are similar to those found in, for example, Islamic art.
 
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In other words, they were cherry-picking data to support a concept from Jungian mysticism and crediting that concept with explaining mathematics.
 
Almo said:
Wow Steve... That mandelbrot is incredible. That shape has 7 arms... prime number!
Click to expand...
Hmm.....how do you count "arms" on a fractal?

I thought that was the idea: That it went on and on and on and on and on and on and on and on....

And then some.

;)
 
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