# Chaos theory schematic

Ian writes –

In making an electronic circuit exhibiting chaos, one is essentially making an analog computer for the differential equations describing the system. This means that circuits that can differentiate a voltage are needed. In practice, it is convenient to actually do this with electronic integrators, the idea being that the input of an integrator is the derivative of its output. In addition, a nonlinear circuit element must be incorporated, as linear systems cannot be chaotic.

Chaos theory schematic – [via] Link.

## 24 thoughts on “Chaos theory schematic”

1. Evil Paul says:

I saw a link to this on theNarbotic blog, which you linked to last week with the simple vactrol. It would make a great synth module for generating semi-random control voltages.

2. gerald says:

Here’s a link to a video of one of Ian’s chaos boards in action:

3. shea says:

this is not a comment but a question i still dont get what chaos is!!!!!Can you give me a easy answer cuz im only 12 and have no clue wut it is!!!!!!I am NOT doing a report but i need 2 know!!!!!!!!!!

4. AP says:

shea, try looking it up on wikipedia.

5. DonH says:

Usedta make circuits sorta like this for fun, but lower BW, used the non-linearity of a lightbulb filament at different temps. This way people could see the light.

Chaos, Shea, is the third form of behavior. Linear behavior, is epsilon > delta. A control input results in a proportionate response in the controlled item. If one uses a smaller stimulus, he derives a proportionally smaller response. Noise is another theoretically possible type of behavior. The item just bops around all over the place without regard to any cofunction, even the prior behavior of the item. Perfectly decoupled behavior, that is observable, is impossible, but represents a conceptual limit. Chaos represents behavior between these extremes.
A fun and simple chaos machine can be constructed out of a couplea dowel rods, for concreteness, lets say 1/4″ in diameter, say 18″ long. Screw screw eyes into the end of both rods, and attach them with a couple inch loop of string. Clamp the one stick horizontally so that the other droops vertically. Attach a disc magnet to the far end of the drooping stick, so it makes a pendulum. Now, were one to deflect the stick, it would swing back and forth, coming to rest over time. The swinging of the stick would be less and less, logarithmically over time, for some natural reasons if one were to give it some thought. Place the apparatus over a board. Have the board be about an inch below the bottom of the pendulum. Now, place some other disc magnets at ‘random’ loci on the board. Now, when one deflects the pendulum, it bounces around in complex patterns before coming to rest. Do this, its quite fun and requires only the spending of a few bucks at radio-shack and the hardware store. Grossly, the behavior of the pendulum is the same, in that it eventually comes to rest as we have constructed a dissipative system and are only energizing it initially. But the pattern our pendulum takes on its way to the resting state becomes far more interesting! Very small changes in the initial condition can result in vastly different behavior a little while after releasing the pendulum! This is chaos. The non-linear element here is the fact that magnetism diminishes as a force proportionally with distance by a squared factor, as do most natural forces.

6. Collin Mel (aka Narbotic) says:

Dang – Now I really have to get my jerkster up and running.
Thanks for the reminder!

7. WhatNo says:

CHaos is random, make a random number generator that can do some kind of random arithmatic, that is chaos theory. WTF are these people on? double twirling mendlebrot setS? Ok, to those that think that Chaos is deterministic , you are on crack, put down the crack pipe. the whole world is Probabalistic. Everything from quarks to random sweerving of solar winds hitting our Power grid. Its random, and probabilistic. you can calculate these probabilities use Quantum physics. But for this guy to make some kind of deterministic circuit, its not CHAOS, this is religion and believing in GOD is what this guy does. Like we are all some cogs in a big deterministic wheel spinning towards our ‘known outcome by the almighty’.

come on people use your heads. we know that these probabilities are calculable, study your sequencdes and series Calculus 6 7 8 9 before you make funny circuits not using RANDOM generators.

Its funny how many people think chaos theory is deterministic…there are only probablistic outcomes, skew curves with integrands of sequences and series… The Fibanacci sequence…etc..

once again, We all know that there is no such thing as FATE (or GOD). we are not some COG in a machine thats grinding to a determined outcome. there is a probablistic outcome that may be visible through some sequences and series..

the butterfly flapped its wings, and the tornado happend. But in every playing of these events throughout eternity along every dimensions in parallel universe’s.. the probabilities/possibilities are ENDLESS…NOT DETERMINED…PROBABILISTIC

as HUMAN we can use quantum interference to view these probabilities..but none-all could happen. Just like thoughts and choices in your life. Each choice leads to a parrellel universe, in an infinite 4d picture of roots branching in every direction, these parallel universe’s exist and continue on for infinity. Just because you made the other choice, does not stop that reality from taking place through Quantum Interference..

If you can think of interference as you are standing at the edge of a cliff, and looking over into the cliff you can visualize yourself jumping off and falling an dhitting the rocks. So you dont jump. that is interference.

8. skab says:

to WhatNo

~You’ve got my mind reeling. I just have some questions. What “allows”….or how did we “get”, “aquire”, “accept”, “create”….or whatever, the ability to have quantum interference? Why should that even exist? Why should we even get as close as having a probabilitical view of the how things are going to turn out? How doesn’t chaos, randomness, and noise “take over” the universe? What holds it back? What keeps it in line? How are we able to even view the possibility of its existence? How is it that pattern and noise can co-exist without there being a something….maybe a God….?

9. Whatno says:

to skab

I love Electrical Engineering and the Philosophy of Electronics (which is what ALL those who practice SCIENCE are, Philosophers of NATURE..or whats called a NATURAL PHILOSOPHER) starting with V=IR , Cause=Action/Reaction V=I/R or soemthing like that, Im not going to go looking throuh my first year books for the natural philosophy parts in the beginning..

Chaos,randomness, and noise are in control of this universe, we are merely riding the planet. About Quantum interference, its used for teleportation of data using parrallel universe computers. 2 atoms have what Einstien described as “Freaky at a distance”, behavior where when observed. All atoms have whats called a SOUP of electrons constantly everywhere around their body, and the idea is that 2 atoms of the same substance will communicate their position when observed…theoretically…anyways Teleportation is 100% complete, and it wont be long now till the first Quantum computer is made.

Esencially it goes back for debate over the last 300 years, where we think of light as both particles and waves..one man Thomas Young devised the double-slit experiment to prove that light consisted of waves. Although the implications of Young’s experiment are difficult to accept, it has reliably yielded proof of quantum interference through repeated trials

To the Human response, Its all about FEAR. interference and all life is driven by fear. I tried to argue with a Philosophy professor who had double doctorates about why FEAR does not control everything and maybe that LOVE could be a controlling factor, he replied simply to every probablity i could tell him, “Nope ruled by fear” I would ask if you were presented with an Abyss, and ont he other side is LOVE, and you knew you could not make it, and jumped across for love, is that not defeating fear?. No because obviously your need to procreate is part of the reason to FEAR death, and to maybe overcome that FEAR of death, for the FEAR of dying genetically forever, which I believe instinct has instructions for you, to procreate. All those questions you asked revolve around FEAR. preservation of life etc..

Hawking left it open for us at the beginning of time, maybe something created the Superforce that was once all forces of nature (magnetism, fire, gravity etc…) But we are too filled with FEAR maybe to find what created these forces and can leave the UNKNOWN to god. Mostly the idea of God comes from fear of the unkown. and Deterministic ideas are likewise. Obviously if we follow these ideas of chaos theory , then Free will does not exist?

but ya, to get back to the topic, Chaos is not deterministic, its probablistic, life is not deterministic, the controls are the decisions people make which branch reality, and each are randomly sequencial.

All this talk of chaos theory goes to the Idea that we have Free will. How can people have free will if this is what you are saying, that Chaos Theory is Hard Determinism. (going further and saying that humans have no control via their actions is Fatalism)

if anything its Quantum probabilities… we should be smart enough to know this now. That wait a minute, We know enough about contemporary physics and qauntum mechanics to say that the world isnt Deterministic, its random/swerving. That probabalisticlly we can have this tornado end up in these 10 million locations…from the results of the butterfly flapping its wings..m,aybe some new type of science will come, like Probablistic determinism

all the circuits people make and the songs they make using ‘chaos theory’ as it is defined now is not chaos, its manipulated deterministic functions, moving in steps. But then again you can say that those seemingly random movements are calculable by Sequences and series that are determined. In my opinion Chaos theory is probabilistic, and cannot be determined to one value or even spoke of using the word Determined. It can be determined to One probability formula that could be 100 Trillion deep sequence. I dont hold all the answers nor do I proport to know.

it might be Probabilistic Determinism

10. WhatNO says:

from skab”
You’ve got my mind reeling. I just have some questions. What “allows”….or how did we “get”, “aquire”, “accept”, “create”….or whatever, the ability to have quantum interference? ”

Through human knowledge. The combined , built upon product of study and learning to reveal the unknown. and not Leave all the Unkown to simply ‘GOD DID IT!!’. I think this debate really relies heavliy on RELATIVE and absolute defiinitions. God is Relative. Absolute is Gravity. ie: Gravity is a force that pulls objects toward one another, measurable quantifiabl…or that Gravity is a force of GOD?

Why should that even exist?
-It exists through the adaption of multiple species and Protozoah to reach us. Multi-celled complex organisms. The first DIRT on the earth was a clay porous substance with an envelope allowing Salts to pass through. in the ARcaen era.

Why should we even get as close as having a probabilitical view of the how things are going to turn out?
-Through built upon human knowledge we reveal the unknown

How doesn’t chaos, randomness, and noise “take over” the universe? What holds it back? What keeps it in line?
-it is in control. By the world/universe and the reality of perception. An island in the sea somewhere 1000’s of years ago exploded and went under in a gigantic eruption causing a huge Tsunami to rip across the whole world , and the axis of the earth underwent a 1 degree change in orientation due to this eruption, causing increasing melting in the polar caps. Since the Ice age the polar caps have been melting. Your perception holds it back, and Reality keeps it in line, the physical limitations of forces(ABSOLUTE).

How are we able to even view the possibility of its existence?
-through the adaptation of cells to phsyiological/emotional stimulii. We evolved. From males with large brows to protect the eyes for hunting and limited speaking skills to hunt efficiently, brain mapping based on last visited locations. Women evolved from sitting around the campfire talking and talking and talking eventually developing language from grunts/clicks/pops, or gathering berries., that is why they have such ability in communications.

How is it that pattern and noise can co-exist without there being a something….maybe a God….?
-the only something is the unkown, god/whatever you call it.. and once we find that abyss of blackness from starring at the abyss long enough, it will stare back at you. and maybe , just maybe we will have some theory about it and some unifying theory of everything.

11. WhatNo says:

Before the discovery of quantum effects and other challenges to Newtonian physics, “uncertainty” was always a term that applied to the accuracy of human knowledge about causes and effects, and not to the causes and effects themselves.

12. wonder-wheeler says:

There are things that are rational and knowable precisely. Such as arithmatic, Newtonian physics, tides, clockworks, and when there will be a full moon.

Then tThere are things that are not precisely knowable, but can still be estimated by some probability. Such as the branching of a tree, swirls of smoke, behavior of clouds, when an earthquake will occur or how and when concrete will crack. Or when your old lady will be receptive to sex…