Pseudonymous university student “CheeenNPP” has developed a personal computer with a change: it is really analog, instead than electronic, and serves to address Lorenz system equations — supplying butterfly-like Lorenz attractor answers as its output.
“One of the main applications of analog circuits is to resolve mathematical issues, this kind of as making a circuit corresponding to a non-linear differential equation and examining the phase airplane attributes of it by observing its output voltage with an oscilloscope or analog plotter,” CheeenNPP describes of the project. “I will take a well known non-linear differential equation, the Lorenz Attractor, as an illustration, and clearly show the complete procedure of fixing it with an analog circuit.”
There is no processor in sight, but this analog pc can address Lorenz procedure equations even so. (????: CheeenNPP)
A technique of a few equations created by Edward Lorenz, Ellen Fetter, and Margaret Hamilton in 1963, the Lorenz system delivers a simplified mathematical design of atmospheric convection primarily based on a two-dimensional fluid layer which is warned from below and cooled from earlier mentioned. It really is most well known for the Lorenz attractor solution family, which makes a sample not as opposed to the wings of a butterfly — and it’s these solutions CheeenNPP’s analog laptop or computer is built to give.
“Integral: use [an] inverting integrator circuit, but temporarily discard the resistor, which is equivalent to integrating the enter latest and multiplying by -1,” CheeenNPP points out of how their development is effective. “Multiplying by -1: use the inverting amplifier and established the two resistors with the exact benefit. Addition: use present-day summation alternatively of voltage, so the kind is more simple. Multiplying by a regular k: use a resistor with a resistance of 1/k, the voltage throughout it is transformed into a current and output as a final result. Multiplication: implemented applying a focused voltage multiplier.”
The underside of the board hosts incredibly neat solder inbound links alongside with jumper wires. (????: CheeenNPP)
Following LTSpice simulation to demonstrate the notion, CheeenNPP established about making it on a prototyping board — ensuing in a astonishingly compact creation with a maze of solder and jumper-wire one-way links beneath. Related to an oscilloscope, the acquainted winged pattern of a Lorenz attractor is straight away seen.
“The phosphor afterglow of the analog oscilloscope […] has a really illusory and ethereal elegance,” CheeenNPP says, “just like the elusive chaos implied by the Lorentzian attractor.”
A circuit diagram and additional information and facts on the job is accessible on CheeenNPP’s Hackaday.io web page.