> A fascinating fact is that the oscillation frequency is rather stable at ~9.9Hz as it mainly depends on gravity and diameter of the flame.
This reminds me of when I first heard about Dolbear's law by which you can get an approximate measurement of the air temperature using the number of chirps per minute from a cricket.
Maybe you could also use the spinning fan from the computer that makes all these calculations, as another frequency reference. Although I'd want that particular calculation to be done in constant time, to avoid potential instability or hunting oscillation.
In the late 1980s I did an electrical engineering internship in a coal-fired power station over summer vacation. The gas furnace igniters ran continuously, but how do you detect presence or absence of burner flames against semi-apocalyptic background of ignited pulverised coal dust being air-blasted into the furnace? Have a little window and photosensor pointing at the burner flame and FFT. No spectral component spike at xHz (IIRC x ~= 13? -- it's a burner flame, underlying dynamics not same as for candle wick) --> ringing alarms, flashing lights.
Thank you for mentioning this! Indeed, a practical application of the flame oscillation research is fire detection and monitoring of combustions processes. I should have mentioned this somewhere.
Bingo. We certainly learned about Cooley-Tukey in undergrad back then. That power station was 100% Hitachi Heavy Industries turnkey. The control rooms had Hitachi mainframe and some minicomputers running proprietary real time OS (I guess). These were the days when the video controller for a colour industrial process control raster display CRT was a waist-high cabinet. So you'd transduce the flicker and then transmit it via analogue current loop to a rack in the control room annex, convert back to voltage, A/D it... and crunch the FFT on one of the control room computers. Something like that. Cheap distributed compute just wasn't a thing at the time.
That is awesome. And I am so sad an individual that my first thought was of a software plug-in that would use this frequency to generate realistic candle-flicker effects.
To continue this tangent, legend has it that some of those battery powered tea candle lights actually reuse the chip from cheap music playing trinkets. If you replace the yellow LED with a speaker, you might hear beepy christmas music or happy birthday.
I've never found one myself (most of them have a better candle simulation chip than that), but they are apparently out there.
In strings of programmable LED lights every single LED is actually an LED combined with a computer. This allows the LEDs to be addressed individually without loads of wires.
While technically a PIC12 is a computer since it has I/O, tiny storage, a PC and an ALU - it’s hard to even think of it in the same category as what most think of as a computer. IMHO the takeaway is more what the bare minimum it takes to be a computer, which isn’t much. (In other terms, a PIC does not meet the DOOM threshold).
PICs are so old and rudimentary that they started out as peripheral controllers for “real” computers in the 70s. It turns out you can do some useful embedded stuff with a basic chip, but even the newest of these are on 30 year old semiconductor tech at this point.
That may sound jaded, on the other hand I do find mass production of modern level integration and speeds to still be marvelous.
And as an EE, the “white” LED in the candle is more interesting than the uC!
Chaotic circuits are neat, but they are actually not random (their output distribution is not uniform or gaussian). And candles are not random either :)
> "More in details, Ando and Graziani demonstrated that the Chua's circuit can be used to generate either a gaussian or a uniform white noise. To do this, they investigate the statistical and spectral characteristics of the signals generated by a Chua's circuit with respect to different values of the parameters α and β. They then applied the x^2 method to determine which set of parameters leads to a signal having the statistical and spectral characteristics more similar to those of either a Gaussian or uniform noise. By using this method, a signal with a Gaussian-like distribution is obtained with a confidence of 95% for this set of parameters: ..."
They've got charts of the probability density functions for each that seem reasonable to me.
Nice, I was not aware of that! Quite interesting. Thank you for the source.
It seems to be a corner case. As I learned to know them, chaotic circuits have unpredictable cyclic behavior. Chua's circuit typically follows an oscillatory behavior with a double attractor.
If true randomness is the goal, it is much easier to use other sources of randomness like avalanche transistors, jitter of ring-oscillators in the analog domain or LFSRs if you are in the digital domain.
I think the main confusion for analog implementations of chaotic circuits is that they often have an inherent source of noise (e.g. johnson or flicker noise of resistors, transistors) which will be amplified into large changes by the sensitivity of the system to initial (and also intermediate) conditions.
So the actual implementation has an unpredictable behavior, but this is because the randomness of the components is amplified.
I don't know what the most obvious distinction between a chaotic analog circuit and a TRNG is. For me it was always obvious that any kind of visible structure in the trajectory (the attractors) contradicts randomness. But whenever people see Chua's circuit brought up, there are lots of commends regarding random number generators. It turned into a bit of a pet peeve of mine.
I don't know much (or really anything) about circuits and circuit noise.
There is a long history of deterministic pseudo RNGs, which you may already know about. https://en.wikipedia.org/wiki/Pseudorandom_number_generator. These are sometimes chaotic. In this line of thinking, a thing that generates unpredictable noise and adds chaos would make probably a good hardware PRNG.
But the chaotic part is not actually random (although it's hard for attackers to predict). And whether the noise is random depends on a bunch of physics.
But if this has gotten to the point of a pet peeve to you, you might be interested in Randomness Extractors (https://en.wikipedia.org/wiki/Randomness_extractor) which are a way of thinking about questions like "we have an unpredictable source of bits, but it's not as random as it seems... how can we extract actual randomness from it?"
For example, extractors can take low quality somewhat random non-uniform (or non-gaussian) output and use it to create high quality uniform (or gaussian output).
Related to this, I once read that the reason nearly every car alarm in the 1990-2010 approx era had the same pattern of awful sound patterns was that they all simply used the same off the shelf sound IC which was produced in such quantities as to make any custom option untenable.
The “car alarm sequence” of 10s patterns was just the self-test demo program for the sound chip.
I believe they were the HK628 and UM3561 chips which were launched in the 1980s for toys. You can actually hear that alarm sound on some toys from that decade. They were simple chips that stored 8-16 preprogrammed sounds and the urban legend is that the car companies just kept the alarm demo sound (I think there were two different ones). The chips ended up everywhere: toys, care, appliances, industrial machinery, etc.
Very neat! I've also seen that some will use Linear Feedback Shift Registers [0] for the candle effect, or maybe that's the same thing you're talking about.
Edit: I see the article in a sibling comment makes note of this too.
The self-trimming wick is the trick. Before that was invented, people had to use special scissors to trim the wick and avoid uncontrollable large (and flickering) candle flames.
Not just flickering; smoking badly as the underheated, unburnt parts roasted outside the flame.
Weirdly, the trick wasn't in changing the wick material to burn better, but changing their shape so they curled over (and remained marginally in the flame until burnt) instead of just sticking straight out: rectangular instead of circular braided string.
I have recently become quite fascinated with how much of what we use daily relies on the laws of physics always working the exact same way. This is a wonderful example of that.
> Now, it’s a curious thing that we try to emulate the imperfections of candles. After all, candle makers have worked for centuries (and millennia) on optimizing candles NOT to flicker?
This reminds me of teenage me circa 1990 exploring electric guitar distortion and having an interesting conversation w/ my dad, who'd done a pretty serious paper on eliminating audio distortion as part of his CSEE degree from MIT.
Agreed, I kept reading through to the end for this. Arguably the most interesting part of this article is "Candle flickering is surprisingly regular and precise" but then they don't actually tell us how precise... Author! We demand satisfaction!
While visiting a friend in Russia I was perplexed by the candle in his flat - it had zero flicker, was stable and unmoving. Eventually I learned how they heated the flat, with water flowing through pipes and heat radiation - so little to no air movement.
No, central heating + radiators are somewhat region specific. For example Australia runs almost entirely on split system reverse aircons and electric heaters.
In northern North America forced-air natural gas is pretty for single family homes. You have a gas furnace that blows heated air through ducts. It's supposed to be relatively inexpensive compared to electric baseboards, presuming you have all the natural gas infrastructure (or a big tank outside).
Same, I had to Google it too but didn't even understand the pictures since they were so alien.
Eventually found this page [1] which includes a basic description:
A baseboard heater is a convection heater. In such heaters, cold air coming in from a window enters the heater through a vent and hot air is dispersed through metal fins that are heated through electricity.
But it's still confusing because if it's cold outside (=you need heating) why would you have your window open to let in the cold air? That would also make your already-heated air escape ... duh.
Agreed, it's amazing how something that "feels" like it would get the same solution everywhere it's needed still does not, due to cultural differences, history, and stuff.
My Massachusetts home has both radiant floor heating (water pipes in floor) and baseboard water pipe heating (separate part of the house). My son’s New York home has radiators driven by hot water. I can’t recall a home where heating was vented air and not circulating hot water in North East USA.
Faraday did a whole series of lectures about a single candle, essentially covering a surprising amount of physics and chemistry. Super simple and fascinating: https://www.gutenberg.org/ebooks/14474
But its not trivial at all, its a complex fluid dynamics problem. I stumbled upon all the "coupled candle oscillators" literature when I was looking for a shortcut to a semi-physical candle model. But there is no easy way out...
seems like a very complicated simulation problem. i'd be surprised if you could derive from first principles.
you need to model the atmosphere as environment, heat flow, wicking action, chemical reactions, fluid dynamics under gravity. Then model human perception to turn the spectral radiance into a perceived shape.
From the article:
> A fascinating fact is that the oscillation frequency is rather stable at ~9.9Hz as it mainly depends on gravity and diameter of the flame.
This reminds me of when I first heard about Dolbear's law by which you can get an approximate measurement of the air temperature using the number of chirps per minute from a cricket.
https://en.wikipedia.org/wiki/Dolbear%27s_law
Combining the two, you can make a thermometer using three candles, a cricket, and a webcam.
Maybe you could also use the spinning fan from the computer that makes all these calculations, as another frequency reference. Although I'd want that particular calculation to be done in constant time, to avoid potential instability or hunting oscillation.
In the late 1980s I did an electrical engineering internship in a coal-fired power station over summer vacation. The gas furnace igniters ran continuously, but how do you detect presence or absence of burner flames against semi-apocalyptic background of ignited pulverised coal dust being air-blasted into the furnace? Have a little window and photosensor pointing at the burner flame and FFT. No spectral component spike at xHz (IIRC x ~= 13? -- it's a burner flame, underlying dynamics not same as for candle wick) --> ringing alarms, flashing lights.
Thank you for mentioning this! Indeed, a practical application of the flame oscillation research is fire detection and monitoring of combustions processes. I should have mentioned this somewhere.
What was the preferred way of doing FFT at that time?
hasn't the preferred way been Cooley-Tukey consistently since 1965?
https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algor...
Bingo. We certainly learned about Cooley-Tukey in undergrad back then. That power station was 100% Hitachi Heavy Industries turnkey. The control rooms had Hitachi mainframe and some minicomputers running proprietary real time OS (I guess). These were the days when the video controller for a colour industrial process control raster display CRT was a waist-high cabinet. So you'd transduce the flicker and then transmit it via analogue current loop to a rack in the control room annex, convert back to voltage, A/D it... and crunch the FFT on one of the control room computers. Something like that. Cheap distributed compute just wasn't a thing at the time.
this is so cool, thanks for sharing :)
Very interesting article from the same guy where he reverse engineers the randomness of a flicker LED.
https://cpldcpu.com/2013/12/08/hacking-a-candleflicker-led/
I was today years old when I learned that the frequency of a flicker candle flame is ~9.9Hz :-)
That is awesome. And I am so sad an individual that my first thought was of a software plug-in that would use this frequency to generate realistic candle-flicker effects.
To continue this tangent, legend has it that some of those battery powered tea candle lights actually reuse the chip from cheap music playing trinkets. If you replace the yellow LED with a speaker, you might hear beepy christmas music or happy birthday.
I've never found one myself (most of them have a better candle simulation chip than that), but they are apparently out there.
This was 10-15 years ago.
In between they used dedicated ASICS: https://cpldcpu.com/2013/12/08/hacking-a-candleflicker-led/
And more recently simply microcontrollers: https://cpldcpu.com/2024/01/14/revisiting-candle-flicker-led...
What a testament to the might of the global electronic supply chain that entire computers are cheap enough to be in disposable candles.
Single use Vape-pens too. Some of those have displays and Bluetooth.
Insane.
In strings of programmable LED lights every single LED is actually an LED combined with a computer. This allows the LEDs to be addressed individually without loads of wires.
Just to offer an alternate perspective.
While technically a PIC12 is a computer since it has I/O, tiny storage, a PC and an ALU - it’s hard to even think of it in the same category as what most think of as a computer. IMHO the takeaway is more what the bare minimum it takes to be a computer, which isn’t much. (In other terms, a PIC does not meet the DOOM threshold).
PICs are so old and rudimentary that they started out as peripheral controllers for “real” computers in the 70s. It turns out you can do some useful embedded stuff with a basic chip, but even the newest of these are on 30 year old semiconductor tech at this point.
That may sound jaded, on the other hand I do find mass production of modern level integration and speeds to still be marvelous.
And as an EE, the “white” LED in the candle is more interesting than the uC!
https://en.wikipedia.org/wiki/Chua%27s_circuit
Chaotic circuits are neat, but they are actually not random (their output distribution is not uniform or gaussian). And candles are not random either :)
btw, slightley related: https://cpldcpu.com/2020/06/15/building-a-chaotic-oscillator...
> their output distribution is not uniform or gaussian
https://www.worldscientific.com/worldscibooks/10.1142/7200#t...
> "More in details, Ando and Graziani demonstrated that the Chua's circuit can be used to generate either a gaussian or a uniform white noise. To do this, they investigate the statistical and spectral characteristics of the signals generated by a Chua's circuit with respect to different values of the parameters α and β. They then applied the x^2 method to determine which set of parameters leads to a signal having the statistical and spectral characteristics more similar to those of either a Gaussian or uniform noise. By using this method, a signal with a Gaussian-like distribution is obtained with a confidence of 95% for this set of parameters: ..."
They've got charts of the probability density functions for each that seem reasonable to me.
Nice, I was not aware of that! Quite interesting. Thank you for the source.
It seems to be a corner case. As I learned to know them, chaotic circuits have unpredictable cyclic behavior. Chua's circuit typically follows an oscillatory behavior with a double attractor.
If true randomness is the goal, it is much easier to use other sources of randomness like avalanche transistors, jitter of ring-oscillators in the analog domain or LFSRs if you are in the digital domain.
This was a cool post. A few nitpicks for anyone else interested in the topic:
(1) a process can be random without being uniform or gaussian
(2) a deterministic process can generate a uniform or gaussian output
(3) chaotic systems are traditionally deterministic by definition. they're deterministic and are sensitive to initial conditions.
Thank you for your comment, indeed!
I think the main confusion for analog implementations of chaotic circuits is that they often have an inherent source of noise (e.g. johnson or flicker noise of resistors, transistors) which will be amplified into large changes by the sensitivity of the system to initial (and also intermediate) conditions.
So the actual implementation has an unpredictable behavior, but this is because the randomness of the components is amplified.
I don't know what the most obvious distinction between a chaotic analog circuit and a TRNG is. For me it was always obvious that any kind of visible structure in the trajectory (the attractors) contradicts randomness. But whenever people see Chua's circuit brought up, there are lots of commends regarding random number generators. It turned into a bit of a pet peeve of mine.
That makes a lot of sense.
I don't know much (or really anything) about circuits and circuit noise.
There is a long history of deterministic pseudo RNGs, which you may already know about. https://en.wikipedia.org/wiki/Pseudorandom_number_generator. These are sometimes chaotic. In this line of thinking, a thing that generates unpredictable noise and adds chaos would make probably a good hardware PRNG.
But the chaotic part is not actually random (although it's hard for attackers to predict). And whether the noise is random depends on a bunch of physics.
But if this has gotten to the point of a pet peeve to you, you might be interested in Randomness Extractors (https://en.wikipedia.org/wiki/Randomness_extractor) which are a way of thinking about questions like "we have an unpredictable source of bits, but it's not as random as it seems... how can we extract actual randomness from it?"
For example, extractors can take low quality somewhat random non-uniform (or non-gaussian) output and use it to create high quality uniform (or gaussian output).
Wow, I'm clearly behind on my flickering candle LED technology knowledge. Thanks!
Related to this, I once read that the reason nearly every car alarm in the 1990-2010 approx era had the same pattern of awful sound patterns was that they all simply used the same off the shelf sound IC which was produced in such quantities as to make any custom option untenable.
The “car alarm sequence” of 10s patterns was just the self-test demo program for the sound chip.
I believe they were the HK628 and UM3561 chips which were launched in the 1980s for toys. You can actually hear that alarm sound on some toys from that decade. They were simple chips that stored 8-16 preprogrammed sounds and the urban legend is that the car companies just kept the alarm demo sound (I think there were two different ones). The chips ended up everywhere: toys, care, appliances, industrial machinery, etc.
Very neat! I've also seen that some will use Linear Feedback Shift Registers [0] for the candle effect, or maybe that's the same thing you're talking about.
Edit: I see the article in a sibling comment makes note of this too.
[0] https://en.wikipedia.org/wiki/Linear-feedback_shift_register
I never thought it would be as regular as that graph and thought it was random. The world around us is so fascinating.
and is it slower or faster on the moon? oh wait...
Assuming you had enough oxygen to waste on this I don't think it says if it would be faster or slower. I wonder which it would be?
The beginning of an alternative-universe candle computer that could've been used in the past.
> Todays candles have been optimized for millenia not to flicker.
Where can I learn more about that? My google fu is failing me.
The self-trimming wick is the trick. Before that was invented, people had to use special scissors to trim the wick and avoid uncontrollable large (and flickering) candle flames.
https://en.wikipedia.org/wiki/History_of_candle_making#Indus...
Not just flickering; smoking badly as the underheated, unburnt parts roasted outside the flame.
Weirdly, the trick wasn't in changing the wick material to burn better, but changing their shape so they curled over (and remained marginally in the flame until burnt) instead of just sticking straight out: rectangular instead of circular braided string.
Inventions like those fall into my weird mental category of "I should investigate and appreciate these just in case I ever get stranded back in time."
I have recently become quite fascinated with how much of what we use daily relies on the laws of physics always working the exact same way. This is a wonderful example of that.
you might like https://en.wikipedia.org/wiki/Noether%27s_theorem
> Now, it’s a curious thing that we try to emulate the imperfections of candles. After all, candle makers have worked for centuries (and millennia) on optimizing candles NOT to flicker?
This reminds me of teenage me circa 1990 exploring electric guitar distortion and having an interesting conversation w/ my dad, who'd done a pretty serious paper on eliminating audio distortion as part of his CSEE degree from MIT.
> as it mainly depends on gravity and diameter of the flame
So cannot be used on a ship. Bummer.
Our sea-faring ancestors wouldn't be happy with this clock.
> cannot be used on a ship.
TIL there’s no gravity on ships. That’s why they float.
https://en.wikipedia.org/wiki/Marine_chronometer
Space-ship, maybe? :P :)
There's lots of gravity in space too.
I want to know the precision of that clock!
Agreed, I kept reading through to the end for this. Arguably the most interesting part of this article is "Candle flickering is surprisingly regular and precise" but then they don't actually tell us how precise... Author! We demand satisfaction!
We should buy a bunch of candles and monitor them and determine the Allan variance.
Came with the same thought!
While visiting a friend in Russia I was perplexed by the candle in his flat - it had zero flicker, was stable and unmoving. Eventually I learned how they heated the flat, with water flowing through pipes and heat radiation - so little to no air movement.
Isn’t it like this mostly everywhere ?
No, central heating + radiators are somewhat region specific. For example Australia runs almost entirely on split system reverse aircons and electric heaters.
In northern North America forced-air natural gas is pretty for single family homes. You have a gas furnace that blows heated air through ducts. It's supposed to be relatively inexpensive compared to electric baseboards, presuming you have all the natural gas infrastructure (or a big tank outside).
I will Google but wanted to point out that I have no idea what "electric baseboards" are.
It's funny how different houses are around the world. Even in similar latitudes/climate.
Same, I had to Google it too but didn't even understand the pictures since they were so alien.
Eventually found this page [1] which includes a basic description:
A baseboard heater is a convection heater. In such heaters, cold air coming in from a window enters the heater through a vent and hot air is dispersed through metal fins that are heated through electricity.
But it's still confusing because if it's cold outside (=you need heating) why would you have your window open to let in the cold air? That would also make your already-heated air escape ... duh.
Agreed, it's amazing how something that "feels" like it would get the same solution everywhere it's needed still does not, due to cultural differences, history, and stuff.
[1]: https://www.cadet.glendimplexamericas.com/en-us/articles/ele...
Maybe it’s single glazed windows so it’s talking about air that has been cooled by the massive heat loss there?
My Massachusetts home has both radiant floor heating (water pipes in floor) and baseboard water pipe heating (separate part of the house). My son’s New York home has radiators driven by hot water. I can’t recall a home where heating was vented air and not circulating hot water in North East USA.
I've never had a house heated with pipes in the US.
Circulating hot water radiators are pretty common in older cities/neighborhoods in the US.
But I suspect the Russian example was radiant heating in the floor slabs, which will cause less air convection than hot water pipe radiators.
What a wonderfully hacky project!
Noob question: How were the diagrams created?
Very cool. I've always wondered what the shape of a flame is and how one could use physics to derive it. anyone have any leads for this?
Faraday did a whole series of lectures about a single candle, essentially covering a surprising amount of physics and chemistry. Super simple and fascinating: https://www.gutenberg.org/ebooks/14474
Look up some YouTube videos of candles or lighters used in zero-gravity. It’s a sphere.
The candle shape on earth is caused by the weight of the air.
The third reference from the article provides some pointers (see also references there).
https://arxiv.org/pdf/1803.10400
But its not trivial at all, its a complex fluid dynamics problem. I stumbled upon all the "coupled candle oscillators" literature when I was looking for a shortcut to a semi-physical candle model. But there is no easy way out...
Thank you! And appreciate the TLDR.
seems like a very complicated simulation problem. i'd be surprised if you could derive from first principles.
you need to model the atmosphere as environment, heat flow, wicking action, chemical reactions, fluid dynamics under gravity. Then model human perception to turn the spectral radiance into a perceived shape.
Or take a candle onto the ISS. Which they did.
My mind is blown candles flicker at a fixed rate
Are we absolutely sure we're not in "the matrix" ?
I believe it's depending on the 3 candles used in the example and their proximity to each other, etc
+ room air currents.
Next somebody tells us that lava lamps have a regular component to them.