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Home Brew Analog Computer System

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GK:
Thanks for the book list - I'll check them out. You are right about the heavy math in most of these texts. Analog computation was all about implementing electrical analogs of physical systems of which the first step is to formulate a mathematical model for the physical system; the analog computer then solves the mathematical model. So you can't really get around the maths! I can't pretend to have my head fully wrapped around even a tenth of it all but that is something I plan to rectify to some degree with the aid of this machine I'm building.

From that book list I posted, the titles numbered 13, 21,23 and 24 are largely devoid of really heavy math as they are concerned almost entirely with the engineering and design of the electrical components and circuits of which analog computers were comprised; they are texts on practical analog circuit design that, despite their age, should be on the bookshelf of every budding analog designer, IMO. Although the technology has moved on the fundamental principles given exhaustive treatment remain the same. Just for example the Korn & Korn volumes contain some of the most thorough analysis of sources of error in operation amplifier circuits and the most succinct and practically detailed explanation of dielectric absorption in capacitors I have found so far.

BTW, would you be interested in selling those sine/cosine pots?





     

GK:
Well, finally, here is the Lorenz Attractor in 3-D projection with variable angles of rotation (the 3-D projection unit in action). I have to say that I am quite happy with the way the synthesized sine/cosine potentiometers worked out with the 8-bit digital pots and the sine/cosine look up table. The 1 degree step resolution and 8-bit accuracy gives a fluid variation in display that is, for all sakes and purposes, totally analog as far as I as the operator can discern. In all honesty the Lorenz Attractor probably isn't the best 3-D "object" to demonstrate the operation of the projection unit, as it is a bit complex and an interpretation of the display isn't intuitively obvious as it is with simpler shapes and objects, such as the assorted springs I posted screen photos of a few posts previously.   



Here is a simplified schematic of  the initial, prototype projection unit. It is based on the basic 3-D projection principle outlined in chapter 9 (Multi-Dimensional Displays) of Analog Computing At Ultra High Speed, D M.MacKay, M E. Fischer.



 

woodchips:
Hi, yes, you are definitely correct about the maths! But, does it have to be so inpenetrable? About 30 years ago DSP chips appeared and I was designing the boards but they looked interesting so started to learn about signal processing. I never really got anywhere. Not so long ago I bought the book by Abbott, phew, Fourier transform with a pencil and ruler!!!!! But why couldn't all these wonderful DSP teaching texts have done the same thing?

I have found that if you want to learn something then any book published after the mid 1960s won't be of any help, they seem to have just swallowed formula and regurgitated them. Just buy lots and lots of books, they all have something of interest in but occasionally you hit a masterpiece, your Korn books for example. My interest was electromagnetism so not really relevant here, did end up with about 200 books though!

Yes, how many of the sine cosine pots did you want? Not certain how many I have got, in the middle of a serious sort out.

GK:
Well, I've managed to design my 3-D projection unit without them now, but I could probably eventually find a use for two or three. What would you want for them?

GK:
Well, after a couple of late evenings of tearing out hair and banging my head against the table I have finally managed to work out a practical and functional electrical analog for the Rössler Attractor.

http://en.wikipedia.org/wiki/R%C3%B6ssler_attractor

The Rössler Attractor is somewhat similar to the Lorenz Attractor, but simpler, and 2 of the 3 coupled differential equations that describe it are linear. However designing a functional electrical analog of the Rössler Attractor was a bit of a challenge due to the way the variables scale and the resultant hyper sensitivity of the circuit to DC offsets (particularly those of the single multiplier stage required). However I succeeded in the end and here is the result:

The Rössler Attractor, being a simpler display that the Lorenz attractor, much better shows off the operation of my 3D projection unit, I think. Also note that I have included a "Chaos potentiometer" into the circuit, which permits me to linearly vary the "d" parameter from a high point at which oscillations cease, down to and through and beyond the point at which the oscillations begin to become chaotic. This is shown in the video.



Here is the complete setup (there is a quad op-amp hiding behind the "chaos pot"):


 

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