Sierpinski pattern generator

PHOBoS

I was searching for some Sierpinski triangle images when I stumbled upon the following image

Besides noticing that it's boolean logic I also realized that it's quite a nice pattern generator.
The (A___), (_B__), (__C_), (___D) patterns are the same as the outputs of a binary counter. And the rest of the pattens
are derived from those using AND logic.

I first drew up a schematic using a counter, a bunch of AND gates and a 4 bit mux, but quickly realized that it could be
done much easier without a mux and only 1 (4 input) AND gate. All that's needed is to connect the inputs to either
one of the outputs of the counter or make it high. And this can be achieved using OR gates Cool

.

note: To get the pattern in the same orientation as the example above the ABCD inputs need to be inverted.

Basic Sierpinski pattern generator.gif

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PHOBoS · Posted: Tue Nov 04, 2014 1:33 pm Post subject:

From that basic version I created a more elaborate circuit. (I'll go from right to left explaining it)
The 4-input AND gate is replaced by 3 2-input AND gates (U4b,U4c,U4d). The 4th AND gate (U4a) is used
to create short (clocked) pulses.
The OR gates are replaced with diodes and resistors.
By adding XOR gates (U2, U3) the outputs from the counter and the ABCD inputs can be inverted. This has
the effect that the pattern is rotated.
For the ABCD inputs there are 3 options:
- a switch to force a high or low state
- using the ABCD CTRL inputs
- using the second counter (U1b) to cycle through the complete pattern (auto switch open).

I haven't tested it yet but I did simulate the logic part and that should work. I'm not enitely sure
about the reset section but I think it'll work like this.

When I first found the above image it was on a seperate page but I now found a page which
has other versions aswell using different logic. So I'm thinking of incorporating that into the circuit
too, most likely with some muxes.

Sierpinski pattern generator2.gif

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Sierpinski Pattern generator V2

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blue hell · Posted: Tue Nov 04, 2014 2:29 pm Post subject:

:-) nice find!

PHOBoS · Posted: Tue Nov 04, 2014 6:04 pm Post subject:

So there are a couple of other possibilities besides AND gates:
OR, XNOR, XOR, NAND, NOR, NXOR, NXNOR

OR, NAND, NOR create Sierpinski triangles like using AND
OR is the inverted version of X=1, Y=1
NAND is the inverted version of x=0, y=1
NOR is the same as X=1, Y=1
so adding an inverter to the output will create all those

More interesting is using a XNOR, XOR, NXOR, NXNOR which creates what's called a Hadamard Matrix.

Basic Hadamard Matrix pattern generator.gif

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Basic Hadamard Matrix pattern generator

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elmegil · Posted: Tue Nov 04, 2014 8:43 pm Post subject:

You're being coy. I want to HEAR it Smile

piedwagtail · Posted: Wed Nov 05, 2014 5:35 am Post subject:

Ha! Loving these studies.

Just as we hear of robots and expert software gradually replacing the "professions" lawyers,accountants etc...soon the contemporary jazz drummer with all their rhythm variations will be replaced by Phobos's Hadamard Matrix pulse streams Wink

Flash ADCs /shift registers etc on the ABCDs will make this so powerful...it's easy enough to sing the variations but the real power lies in the ability to change those variations without some clunky intervention.

Robert

PHOBoS · Posted: Wed Nov 05, 2014 7:55 am Post subject:

PHOBoS · Posted: Wed Nov 05, 2014 8:19 am Post subject:

And here's a drone thingy with 2 of the CTRL inputs connected to oscillators running at audio frequencies.
(and a ton of added delay/reverb)

PHOBoS - Sierpinski Drone.mp3

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PHOBoS - Sierpinski Drone

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PHOBoS · Posted: Wed Nov 05, 2014 11:38 am Post subject:

here' s a version that has most of the different gate options.
Easiest way seems to be to use both AND and XOR gates and just switch between them (or you could use both outputs).
This leaves a spare XOR which can be used as an inverter and a spare AND which is used to create short pulses.

Inverting the outputs of the counter is the same as counting backwards so instead of the CD4520 + CD4070 I used a CD4029.
No XOR's on the CTRL inputs this time but they could be inverted externally.

Sierpinski Hadamard pattern generator.gif

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Sierpinski Hadamard pattern generator

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RingMad · Posted: Wed Nov 05, 2014 12:13 pm Post subject:

Wow, The Amazing PHOBoS once again pulls a really interesting circuit rabbit out of his electronic hat Smile

Can you do a Koch snowflake or a dragon curve? Smile

What about replacing the gates with JingleJoe's "4051 ANY gate"? Although I barely remember how that worked or if it's even appropriate. Probably not, sorry.

- james

PHOBoS · Posted: Wed Nov 05, 2014 1:14 pm Post subject:

oops I accidentally hit the edit button on your reply, hope it's restored as it was Embarassed

PHOBoS · Posted: Thu Nov 06, 2014 3:34 pm Post subject:

Here's a mux/anygate version anyway.

Sierpinski Hadamard pattern generator (mux).gif

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Sierpinski Hadamard pattern generator (mux version)

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