Generating The Mandelbrot Set With IBM Mainframes

March 26, 2015 by Brian Benchoff 34 Comments

[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.

Exploring The Mandelbrot Set In Real Time

October 23, 2012 by Brian Benchoff 33 Comments

The Mandelbrot set – the fractal ‘snowman turned on its side’ seen above – has graced the covers of magazines, journals, and has even been exhibited in art galleries. An impressive feat for what is nothing more than a mathematical function, and has become something of an obsession for [Chiaki Nakajima].

Even on modern computers, generating an image of a portion of the Mandelbrot set takes a good bit of time. When [Chiaki] discovered this fractal in the mid-1980s, the computers of the day took hours to generate a single, low-resolution image. Real-time zooming and scrolling was impossible but [Chiaki] made the best of what he had on hand and built Pyxis, a Mandelbrot set generator made entirely out of TTL logic chips (Google Translate here).

The original Pyxis connected to a desktop computer via a breakout box. while a special program toggled the bits and registers inside the Pyxis to generate pictures of the Mandelbrot set a thousand times faster than the CPUs of the day could muster.

Time marches on, and the original logic chip Pyxis is can be easily surpassed by even the slowest netbooks. There is, however, another way to build a hardware Mandelbrot set generator: FPGAs.

A few years ago, [Chiaki] began work on the Pyxis2010 (translation), an FPGA-based Mandelbrot set generator able to dynamically zoom and pan around the world’s most popular fractal. Built around an Altera Cyclone III FPGA he picked up from Digikey for $600 (no, not a dev board, just a bare chip), [Chiaki] began deadbugging his circuit directly onto the pins of the hugely expensive FPGA. A man with a steady hand and no fear if there ever was one.

Instead of connecting his Mandelbrot generator to a computer and using it as a co-processor, [Chiaki] decided he wanted something more portable. He found an old Sony PSP, removed the LCD screen, and integrated it into his circuit. After a careful bit of dremeling and fabrication, [Chiaki] had a hand-held Mandelbrot generator that is able to display images of the world’s most famous fractal faster than any desktop computer.

It goes without saying this build is incredible. The technical skill to build an insanely fast Mandelbrot generator on an FPGA is astonishing, but basing it off a logic-chip based build reaches into the realm of godliness. You can check out a video of this amazing build after the break.

Props to [Ian Finder] for sending this one in.

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Fractal Viewer Can Zoom And Enhance Like On CSI

January 31, 2012 by Mike Szczys 15 Comments

This fractal viewer is a great way to get your feet wet with Field-Programmable Gate Arrays. The project will give you some experience working with video output, user input, and a whole bunch of math and memory management. [Hamster] built it using the Papilio Plus board which hosts a Spartan 6 FPGA. This continues his odyssey into the realm of hardware design; part of which we looked at back in December.

The arcade Megawing for the dev board gives him easy access to the controls needed to scroll and zoom on the fractal design. Calculations to generate the shape are being run at 240 MHz, with the VGA output running at 80 MHz. The device has enough horse power and SRAM to show an 800×600 pixel output with a 60 Hz refresh rate.

We really liked the logic diagram that [Hamster] drew up when planning how the calculations would be handled. It’s not overly complex, but it took us a while to conceptualize how everything fits together. It’s certainly an improvement from his last attempt as we couldn’t make heads or tails out of that flow chart.

If you’re just interested in the pretty shapes and colors there’s a demo embedded after the break.

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FPGA Mandelbrot Fractal Engine

June 7, 2011 by Mike Nathan 24 Comments

fpga_mandelbrot

[Mike Field] has always been interested in the Mandelbrot Set since he first read about it back in the ‘80s. Having coded it on a Commodore VIC20 back int he day, he always returned to the Mandelbrot set when he wanted to try out some new programming technology.

He wanted to delve deeper into the world of FPGAs, so [Mike] figured the best way to do so would be to use one to program a Mandelbrot fractal engine. He started out with a goal of creating a 640×480 Mandelbrot display, but over time, he found that he could push his Nexus 2 FPGA to 800×600. He didn’t stop there, and after tweaking a few things, he was amazed to find that he could push a 1024×768 display from the small board.

He kept a pretty detailed log as he went along, should you be interested in trying your hand at the process as well. Though there is no video of the FPGA in action, there are a few cool pictures showing off his handiwork.

ChipKIT Uno32: First Impressions And Benchmarks

May 27, 2011 by Phil Burgess 49 Comments

Following Maker Faire, we’ve had a few days to poke around with Digilent’s 32-bit Arduino-compatible chipKIT boards and compiler. We have some initial performance figures to report, along with impressions of the hardware and software.

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