Fractals

[Alkatran]

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.

[Complexity]

The best fractal generator I've played with is FractInt, although it has been a few years (they're up to version 20 now, I believe). It may be only for PCs.

http://spanky.triumf.ca/www/fractint/fractint.html

[T'ai Chi]

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.

Yup!

A couple of years ago in Oregon I saw Mandelbrot give a presentation to the general public on fractals. It was really neat!

[Alkatran]

The best fractal generator I've played with is FractInt, although it has been a few years (they're up to version 20 now, I believe). It may be only for PCs.

http://spanky.triumf.ca/www/fractint/fractint.html

Wow, they're talking about taking days to generate them. I stuck with a simple 255 maximum iterations, haha.

[drfrank]

My housemate has a multi-processor demo for his 12 node cluster that calculates up to 10000 iterations - it's pretty sweet :D

[Complexity]

Wow, they're talking about taking days to generate them. I stuck with a simple 255 maximum iterations, haha.
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.

[CFLarsen]

The best fractal generator I've played with is FractInt, although it has been a few years (they're up to version 20 now, I believe). It may be only for PCs.

http://spanky.triumf.ca/www/fractint/fractint.html
Concur. Fractint is by far the best I've seen, too.

[Aquila]

I've always known about fractals and even looked at programs that let you zoom in before....
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".

[MRC_Hans]

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

[Meffy]

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.

[BeholdTheTruth]

Check out lindenmayer systems at...

http://andreea.francu.com/lgrammar/fractals.html

and

http://home.wanadoo.nl/laurens.lapre/lparser.html

[Alkatran]

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".

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...

[steve s]

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. (http://www.ultrafractal.com/) 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.apophysis.org/)

http://www.photochimps.com/gallery/data/604/fract2.jpg

http://www.photochimps.com/gallery/data/604/fract1.jpg

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

Steve S.

[Meffy]

Ooo. Ahh.

[Zep]

Apophysis is VERY nice! Thank you!

[MRC_Hans]

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. (http://www.ultrafractal.com/) 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.apophysis.org/)


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

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

Hans

[Aquila]

I also have no idea why people drawing things that look similar would mean a collective unconscious...
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.

[DrMatt]

In other words, they were cherry-picking data to support a concept from Jungian mysticism and crediting that concept with explaining mathematics.

[Almo]

Wow Steve... That mandelbrot is incredible. That shape has 7 arms... prime number!

[CFLarsen]

Wow Steve... That mandelbrot is incredible. That shape has 7 arms... prime number!
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.

;)

[steve s]

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

Hans


Getting that 3D look in Ultra Fractal isn't always easy. Apparently it only works with basic Mandelbrot and Julia sets (unless I'm missing something.) I'm still in the learning stages with this app.

If you download UF, be sure to go through the tutorials and sample files. The prog is a little complicated up front, but once you learn what everything is for it gets a lot easier.

Steve S.