# Lorenz Attractor

• posted

I built this circuit a few years ago and it works:

I used AD633 instead of MPY634 but otherwise followed the design exactly.

Looking back on it now, I don't understand what the author means by "the equations on the diagram are normalized to 0.1V."

The multiplier output is A*B/10 not A*B/100, so surely the output of U3 is -x*z/10 and therefore:

C * dy/dt = (rx-y-10*xz) / 1e6

and not:

C * dy/dt = (rx-y-xz) / 1e6

What am I missing?

TIA

• posted

Wonder how you'd make that as a screen saver? ...Jim Thompson

```--
[On the Road, in New York]

| James E.Thompson, CTO                            |    mens     |```
• posted

Why reinvent the wheel? Google "lorentz screen saver" there are already several free ones. Art

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"Jim Thompson" wrote in message news: snipped-for-privacy@4ax.com...

BTW thanks for the beer, have a safe flight home!

Cheers

• posted

"Artemus"

** You gotta spell the word right first ...

... Phil

• posted

Thanks, You're quite welcome! Enjoyed meeting you and our chat! ...Jim Thompson

```--
[On the Road, in New York]

| James E.Thompson, CTO                            |    mens     |```
• posted

Cool, I'm about to build one of these! I wouldn't worry too much about what Paul calls the scale factor. One the side he's got the MPY output as A*B/10, so he's got that right.

George H.

• posted

y.

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I'm re-building the circuit using a different multiplier and I need to fully understand the design calculations. I will fish out my old board tonight and check the output amplitudes. I wonder if they differ by a factor of 10? Don't get me wrong - you'll get an owl's face on the 'scope with Paul's component values.

• posted

I believe that the behavior of a really badly squegging LC oscillator is also chaotic. Long before I knew what "squegging" means, I built one and wondered what the funny O-scope trace was. Shortly after I read an article in one of the IEEE magazines about chaotic behavior and hey! -- there was my O-scope trace!

```--
www.wescottdesign.com```
• posted

tly.

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Oh, there's a nice little circuit tweak where you add a pot on the x- channel, so that dy/dt =3D r*Q*x - y -x*z. Where Q is the setting on the ten turn pot (0

• posted

OK. I figured it out. The resistor values are correct. The multiplier outputs are labelled wrongly on the diagram. It is confusing because lower case x,y,z are used for both normalised and un-normalised parameters.

Say X,Y,Z are the un-normalised parameters.

dY/dt = R*X - Y - X*Z

The problem is, Y varies +/- 20 peak to peak.

Paul's circuit scales the voltages down by a factor of 10:

x = X/10 y = Y/10 z = Z/10

dy/dt = (R*10*x - 10*y - 100*x*z) / 10 dy/dt = R*x - y - 10*x*z

The multiplier output is x*z/10 so we need a gain of 100 on this term feeding into the integrator.

1Meg/100 = 10k

The multiplier output is -x*z/10 or -X*Z/1000 not /100.

I tis just the multiplier

>
• posted

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Hi Andrew, I guess that makes sense. Does the 1/10 scaling happen in the multiplier?

My problem at the moment is that I want to make R really big. (200-300) (This moves the thing away from chaos and you can see the period doubling type of behavior before chaos starts.) When I do that the z-signal hits the positive rail. I got a little more head room by off setting my power supply +20 and -10. But not enough. So how do I scale all the voltages down by, say a factor of two? I'm going to try throwing away signal before the multipliers.

George H.

at work on a holiday... attracted to a Lorenz, at least there is no one to disturb me. :^)

• posted

Hi Andrew, I guess that makes sense. Does the 1/10 scaling happen in the multiplier?

My problem at the moment is that I want to make R really big. (200-300) (This moves the thing away from chaos and you can see the period doubling type of behavior before chaos starts.) When I do that the z-signal hits the positive rail. I got a little more head room by off setting my power supply +20 and -10. But not enough. So how do I scale all the voltages down by, say a factor of two? I'm going to try throwing away signal before the multipliers.

George H.

at work on a holiday... attracted to a Lorenz, at least there is no one to disturb me. :^)

_Increasing_ multiplier gain scales x, y, z _down_.

In Paul's circuit, changing R4 and R6 from 10k to 1k would reduce the x, y, z amplitudes by a factor of 10.

Try this:

Version 4 SHEET 1 904 680 WIRE 224 -48 128 -48 WIRE 288 -48 224 -48 WIRE 528 -48 448 -48 WIRE 608 -48 528 -48 WIRE 128 -16 128 -48 WIRE 448 -16 448 -48 WIRE 128 80 128 64 WIRE 448 80 448 64 WIRE 224 160 128 160 WIRE 288 160 224 160 WIRE 528 160 448 160 WIRE 608 160 528 160 WIRE 128 192 128 160 WIRE 448 192 448 160 WIRE 128 288 128 272 WIRE 448 288 448 272 WIRE 224 368 128 368 WIRE 288 368 224 368 WIRE 528 368 448 368 WIRE 608 368 528 368 WIRE 128 400 128 368 WIRE 448 400 448 368 WIRE 128 496 128 480 WIRE 448 496 448 480 FLAG 448 80 0 FLAG 128 80 0 FLAG 224 -48 x FLAG 528 -48 dx_by_dt FLAG 448 288 0 FLAG 128 288 0 FLAG 224 160 y FLAG 528 160 dy_by_dt FLAG 448 496 0 FLAG 128 496 0 FLAG 224 368 z FLAG 528 368 dz_by_dt SYMBOL bv 128 -32 R0 SYMATTR InstName B1 SYMATTR Value V=idt(V(dx_by_dt), 10) SYMBOL bv 448 -32 R0 SYMATTR InstName B2 SYMATTR Value V={S}*(V(y)-V(x)) SYMBOL bv 128 176 R0 SYMATTR InstName B3 SYMATTR Value V=idt(V(dy_by_dt), 0) SYMBOL bv 448 176 R0 SYMATTR InstName B4 SYMATTR Value V={R}*V(x)-V(y)-V(x)*V(z)*{MGAIN} SYMBOL bv 128 384 R0 SYMATTR InstName B5 SYMATTR Value V=idt(V(dz_by_dt), 0) SYMBOL bv 448 384 R0 SYMATTR InstName B6 SYMATTR Value V=V(x)*V(y)*{MGAIN}-{B}*V(z) TEXT -120 96 Left 0 !.tran 0 100 50 TEXT -120 184 Left 0 !.param S 10\n.param R 28\n.param B 8/3\n.param MGAIN

10
• posted

the

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Yup, that's what it looks like.

y,

Yabut, you gotta change the multiplier gain at the same time or you change the equation... (I think.)

That's great! Thanks. I didn't think of spicing it. If you put in R =3D 300 you can see that Z gets up to ~36 volts or so.

Setting a non-standard denominator gain in the AD734, is a bit weird. It looks like I have to trim a resistor for each unit.

George H.

N
• posted

exactly.

"the

U3

multiplier

because lower

Many multiplier (/divider) ICs compute x*y/10*z.

?-)

• posted

much

MP=

Hi, I'm working on this circuit, but it dosn't work at all. Need it for a project and tested everything 100 times. I got the answer to my first question with A*B/10 and not AB/100. What do u mean with 3D in this equation dy/dt =3D r*Q*x - y -x*z? Did not ur circuit work without this poti? Or u used a poti instead of a 35.7k resistor? For which value begins the circuit to work chaotically? I'm using MPY634 and LF412. Thanks, mani

--------------------------------------- Posted through

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Are you using a bipolar power supply? Everything is getting power? At what voltages do the X, Y and Z outputs sit when you power it up? I've still got mine on a white proto board thing. (But it'll be Monday before I get back to work.) (Unless you respond very quickly) Try sending some DC voltages into the multiplier and make sure that it is working... Then you could break open the circuit at other parts... send in some test signal and make sure that the right thing comes out the other side. It's a bit hard to trouble shoot since it only works when all the pieces are hooked together.

The 3-D is about the three different 'coordinates' in the equation. There must be some computer images of this on the web. Normally you just do X vs Y, but there is Z also. Andrew posted a nice spice file.

You don't need the potentiometer, I was just having fun. (It'll be a much nicer project if you give people a knob to turn though.)

George H.

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