# Zooming Through The Mandelbrot Set On An Atari

The Mandelbrot set, according to Wikipedia, is “the set of complex numbers $c$ for which the function $f_{c}(z)=z^{2}+c$ does not diverge.” Even if you don’t understand the mathematics behind it, you’ve likely seen the complicated fractal images generated by zooming in on the border of the Mandelbrot set. [Scott Williamson] not only got this set rendering on an Atari, but managed to create animated videos of the results.

Doing the work was no mean feat. While it takes just 10 lines of Atari BASIC to render the set on an Atari 800, getting the animations made and into a modern video format took much effort. [Scott] used the Atari800Win-PLus emulator to zoom in on a variety of locations on the fractal curve and recorded the results over a weekend.

However, compositing the various frames into smooth-scrolling videos took more effort, with a Python script and `ffmpeg` required to stitch everything together into the results you see on YouTube. The final videos were combined with Atari chiptune music from [Adam Sporka] to help round out the presentation.

The result is reminiscent of an old-school demo, even if everything here was assembled slowly on modern computers from the raw Atari output. We’ve seen other great Mandelbrot feats before, too, like this real-time explorer built on an FPGA. Video after the break.

# Dancing Mandelbrot Set On A FPGA

This FPGA based build creates an interesting display which reacts to music. [Wancheng’s] Dancing Mandelbrot Set uses an FPGA and some math to generate a controllable fractal display.

The build produces a Mandelbrot Set with colours that are modified by an audio input. The Terasic DE2-115 development board, which hosts a Cyclone IV FPGA, provides all the IO and processing. On the input side, UART or an IR remote can be used to zoom in and out on the display. An audio input maps to the color control, and a VGA output allows for the result to be displayed in real time.

On the FPGA, a custom calculation engine, running at up to 150 MHz, does the math to generate the fractal. A Fast Fourier transform decomposes the audio input into frequencies, which are used to control the colors of the output image.

This build is best explained by watching, so check out the video after the break.

# Generating The Mandelbrot Set With IBM Mainframes

[Ken Shirriff] is apparently very cool, and when he found out the Computer History Museum had a working IBM 1401 mainframe, he decided to write a program. Not just any program, mind you; one that would generate a Mandelbrot fractal on a line printer.

The IBM 1401 is an odd beast. Even though it’s a fully transistorized computer, these transistors are germanium. These transistors are stuffed onto tiny cards with resistors, caps, and diodes, than then stuck in a pull-out card cage that, in IBM parlance, is called a ‘gate’. The computer used decimal arithmetic, and things like ‘bytes’ wouldn’t be standard for 20 years after this computer was designed – 4,000 characters of memory are stored in a 6-bit binary coded decimal format.

To the modern eye, the 1401 appears to be a very odd machine, but thanks to the ROPE compiler, [Ken] was able to develop his code and run it before committing it to punched cards. An IBM 029 keypunch was used to send the code from a PC to cards with the help of some USB-controlled relays.

With the deck of cards properly sorted, the 1401 was powered up, the cards loaded, and the impressive ‘Load’ button pressed. After 12 minutes of a line printer hammering out characters one at a time, a Mandelbrot fractal appears from a line printer. Interestingly, the first image of the Mandelbrot set was printed off a line printer in 1978. The IBM 1401 was introduced nearly 20 years before that.