STM32 Gets Up Close And Personal With Mandelbrot

The Mandelbrot set is a curious mathematical oddity that, while interesting in its own right, is also a useful tool for benchmarking various types of computers. Its constant computing requirement when zooming in and out on the function, combined with the fact that it can be zoomed indefinitely, means that it takes some quality hardware and software to display it properly. [Thanassis] has made this a pet project of his, running Mandelbrot set visualizations in different ways on many different hardware platforms.

This particular one is based on an STM32 board called the Blue Pill, which [Thanassis] chose because he hadn’t yet done a continuous Mandelbrot zoom on a microcontroller yet. The display is handled by a tiny 16K IPS color screen, and some clever memory tricks had to come into play in order to get smooth video output since the STM has only 20 kB available. The integer multiplication is also tricky on a platform this small while keeping the continuous zoom function, so it’s limited to fixed point multiplication.

Even with the limitations of the platform, he is still able to achieve nearly double-digit FPS rates with this one. If you want to play around with graphics like this on an STM platform, [Thanassis] has released all of the source code on his GitHub page, but if you’d like to see more Mandelbrot manipulation you can check out one of his older projects where he built a similar project on an FPGA.

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FPGA Used VHDL For Fractals

Over on GitHub, [ttsiodras] wanted to learn VHDL. So he started with an algorithm to do Mandelbrot sets and moved it to an FPGA. Because of the speed, he was able to accomplish real-time zooming. You can see a video of the results, below.

The FPGA board is a ZestSC1 that has a relatively old Xilinx Spartan 3 chip onboard. Still, it is plenty powerful enough for a task like this.

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High-Voltage Fractals

Int 1777, Georg Lichtenberg found that discharging high voltage on an insulating surface covered with a powder, a fractal-like image appears, sometimes known as a lightning tree. Incidentally, this is a crude form of xerography, the principle that lets copiers and laser printers operate.

[PaulGetson] had a high voltage power source from his Jacob’s ladder experiments and decide to see if he could create Lichtenberg figures. Turns out, he could.

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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.

Dancing Mandelbrot Block DiagramOn 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.

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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.

Koch Lamp Is 3D Printed With A Twist

Koch Lamp

[repkid] didn’t set out to build a lamp, but that’s what he ended up with, and what a lamp he built. If the above-pictured shapes look familiar, it’s because you can’t visit Thingiverse without tripping over one of several designs, all based on a fractal better known as the Koch snowflake. Typically, however, these models are intended as vases, but [repkid] saw an opportunity to bring a couple of them together as a housing for his lighting fixture.

Tinkering with an old IKEA dioder wasn’t enough of a challenge, so [repkid] fired up his 3D printer and churned out three smaller Koch vases to serve as “bulbs” for the lamp. Inside, he affixed each LED strip to a laser-cut acrylic housing with clear tape. The three bulbs attach around a wooden base, which also holds a larger, central Koch print at its center. The base also contains a PICAXE 14M2 controller to run the dioder while collecting input from an attached wireless receiver. The final component is a custom control box—comprised of both 3D-printed and laser-cut parts—to provide a 3-dial remote. A simple spin communicates the red, green, and blue values through another PICAXE controller to the transmitter. Swing by his site for a detailed build log and an assortment of progress pictures.

 

HDTV Antenna That Can Hang In A Window

We can’t wait to give this one a try. We’ve got a DIY HDTV antenna hanging out in the attic which was made from some scrap wood and eight metal coat hangers. It works great but it’s pretty ugly and not everyone has an attic to hide it in (not to mention the signal drop caused by the roof shingles). This is a fractal antenna anchored to some clear plastic so you can just hang it in the window and start picking up the over-the-air channels without much effort.

The pattern was modeled in SketchUp then printed out on two pieces of paper. One piece had it printed on both sides, which makes it easy to glue on a sheet of aluminum foil, then follow the pattern on the opposite side to cut out the important parts. The other template was used as an aligment guide when gluing the foil to the clear plastic. A coaxial adapter was then attached using nuts and machine screws. If you build it, let us know how it comes out!