Author Topic: Amazing Mandelbrot app  (Read 622 times)

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Offline daniel1948

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Amazing Mandelbrot app
« on: March 31, 2016, 04:10:03 PM »
A couple of decades ago, more or less, Scientific American published a piece about the Mandelbrot set. While they didn't provide code, they did give the mathematical formula that is the basis of the set and suggested assigning a color to each point in the set based on the math. I was intrigued, and wrote a program in C on my 80286 PC AT clone with math coprocessor chip running MS-DOS. I had Hercules monochrome graphics, which gave much finer resolution than color graphics of the day, but just a single color: each pixel either on or off. Tooting my own horn here, it was quite a slick program. Beginning by showing the entire set, the user could select a any portion by setting vertical and horizontal lines with the arrow keys to create a box, and then the program would calculate the selected frame. It took several hours to run the calculations for any given frame. Some frames were done in a matter of 3 or 4 hours, some took as long as 20 hours, depending on the number of calculations needed.

When I was studying Spanish at the university in around 1994-5, as a student I had access to the workstations connected, I think, to the mainframe computer. I ported the math portion over to Unix on the workstations. I put my parameters on a floppy disk, put it into the workstation, and when it exited just moments later I figured there was a bug and I took it home, and to my surprise, all the calculations were done. A frame that would have taken my 80286 5 or 6 hours, took the workstation/mainframe an eyeblink.

I wanted to modify the program to run fully on the workstation and display in color, but while I could compile and run the math in the terminal, graphics required X-Windows, and that turned out to be more than I could handle, so I never wrote the color version.

Some years later, when I had a Windows computer, and then the iMac, I thought of starting over, but writing software on a multi-tasking system (event-driven programming) was too tedious to be fun, so I never wrote any software after upgrading from MS-DOS.

Which brings me to a couple of days ago when I decided to search the app store for a Mandlebrot app, and I found Frax HD for the iPad and I downloaded it onto my iPad Pro. It is unbelievable! The Pro is so much faster than the 80286 that it creates the set as fast as you can drag your finger across the screen. I hope this doesn't sound like an infomercial (and mods, feel free to delete this if I'm breaking a rule by promoting an app) but the app is well worth the $2 plus tax I paid for it on the app store. The patterns and colors are spectacular. There's also a pro version with more controls, but I cannot even figure out all the gestures on the basic version so I'll probably stick with the basic one.

Lots of fun. Amazing pictures. It also does the Julia set, which is another fractal like the Mandlebrot set, with some similarities and some differences.
Daniel
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Offline brilligtove

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Re: Amazing Mandelbrot app
« Reply #1 on: March 31, 2016, 05:20:24 PM »
Thanks for the info. I'll check it out.
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Offline superdave

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Re: Amazing Mandelbrot app
« Reply #2 on: March 31, 2016, 05:30:46 PM »
I disavow anyone in the movement involved in any illegal,unethical, sexist, or racist behavior. However, I don't have the energy or time to investigate each person and case, and a lack of individual disavowals for each incident should not be construed as condoning such behavior.

Offline HighPockets

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Re: Amazing Mandelbrot app
« Reply #3 on: March 31, 2016, 07:30:14 PM »
(click to show/hide)

Ah Poop. You beat me to it.
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Online arthwollipot

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Re: Amazing Mandelbrot app
« Reply #4 on: March 31, 2016, 10:28:25 PM »
Coulton expressed some doubt when Mandelbrot died whether he should change the lyrics of the song when performing it live:

Mandelbrot's in Heaven
At least he will be when he's dead
Right now he's still alive and teaching math at Yale

I always thought that the best option would be to simply not sing the second and third line - just play the music without lyrics, then come back in with "He gave us order out of chaos..."

Offline daniel1948

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Re: Amazing Mandelbrot app
« Reply #5 on: April 01, 2016, 10:12:25 AM »
I'm not sure that he "gave us order out of chaos." He gave us a mathematical formula with very curious properties, which can be used to create mind-boggling images, with seemingly infinite approximated repetitions.
Daniel
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Offline gmalivuk

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Re: Amazing Mandelbrot app
« Reply #6 on: April 02, 2016, 03:06:06 PM »
Coulton expressed some doubt when Mandelbrot died whether he should change the lyrics of the song when performing it live:

Mandelbrot's in Heaven
At least he will be when he's dead
Right now he's still alive and teaching math at Yale

I always thought that the best option would be to simply not sing the second and third line - just play the music without lyrics, then come back in with "He gave us order out of chaos..."
I'm pretty sure that is what he did, at least in the first performance of the song after Mandelbrot's death.
The world is so exquisite with so much love and moral depth, that there is no reason to deceive ourselves with pretty stories for which there's little good evidence. Far better...is to look death in the eye and to be grateful every day for the brief but magnificent opportunity that life provides.

 

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