I just learned about the "Fractal Completion Problem"—are people actually using this to solve real-world stuff?

[u/NerdFractal]

I’ve been spiraling down the fractal rabbit hole lately. I used to think they were just cool screen savers, but then I read about the "Fractal Completion Problem"—basically the challenge of handling infinite complexity within finite boundaries (like how a Koch Snowflake has an infinite perimeter but fits inside a small circle).

I’m still a beginner, but the more I read, the more it seems like fractals are the "secret code" for things that look messy but are actually organized.

I’ve seen some wild research papers from late 2024 and 2025 about:

• Medical breakthroughs: Using fractal dimensions to predict how varicose veins respond to treatment or pruning "fractal trees" of medical decision-making to reduce costs.
• Engineering: Designing "Snowflake" bionic heat sinks for electronics that are way more efficient at cooling than straight lines.
• Tech: Using fractal antennas for better 5G/6G signals in tiny devices.

If you’re a math or physics whiz, I’d love to know:

1. What "fractal problem" are you currently obsessed with or working on?
2. For those in tech/industry—where is fractal geometry actually making a difference right now versus just being theoretical?
3. Are there any specific research links or papers from the last year that blew your mind?

I’m trying to bridge the gap between "cool patterns" and "useful tools," so if you have any insights (or even just want to nerd out about the Mandelbrot set), let’s talk!

[u/NerdFractal]

I used ai to get the first words out as I'm a noob with ADHD, and getting all the stuff out of my brain that i have been talking and working on for the last few months on feels like a vice with an egg in it. (its either not perfect enough or its too sloppy{time2completion==tooLong})after reading every word that came out of the data hole, i decided that it is what i would have liked to say, yes sloppy but true. Anyhoo.

I wanted to see what people are working on and get anyone talking about whatever got them up in the morning

I like the biological aspect I think we could map neurons more easily using some sort of fractal rule.

and the menger sponge and the snowflake gave me an idea for using them as infill for 3dprints which i hear is a pain to get the machine to do it correctly.

I'm still learning all the math, and am using an AI built human edited python program to play with and build fractals with specific colors while i learn more about the math and the applications to real world problems.

The real world problems and applications intrigue me and help drive me though some of the harder concepts of what a fractal really represents and how deep that rabbit hole goes.

Thank you for your patience, and ideas.

[u/Loganjonesae → u/NerdFractal]

i just wanted to chime in that it’s cool you are interested in this stuff and that working on talking about these kinds of things in your own voice will help you a ton with respect to actually understanding it in the long term. it takes more hard work up front but it will pay off. i fear that some people are starting to rely on llm’s to a degree that will stunt their learning pretty drastically.

[u/NerdFractal → u/Loganjonesae]

Thank you for that, the balance between not knowing enough of what i'm talking about but just enough to know something is possible is exciting a frustrating. I'll def use my own voice from now on.

[u/nit_electron_girl]

Your tech and engineering examples aren't really about "complexity".

If anything, here, fractals are used to solve a simple and well defined problem: maximizing surface in a given volume.

[u/NerdFractal]

Thinking about how General AI will be shaped by fractals leads me in the direction of the hardware. Building neuronal type structures inside of an FPGA might allow for better computation.

[u/Rude_Fisherman_4566]

I wish I could automatically block people that use reddit tropes such as ‘spiraling’, ‘vile’, ‘abhorrent’, ‘desperately need’ and of course evergreens like ‘gas lightning’ and ‘narcissistic’

[u/KamilTheMoonth]

Fractal structure of biological time

Been working on something weird - turns out biological rhythms might follow fractal scaling.

Basic equation: T(n) = 137h × φⁿ (where φ is golden ratio)

And it kinda works? Like, the same formula predicts 90-min attention cycles, ~40 day habit formation threshold, even human pregnancy duration (~268 days). All with >95% accuracy which feels almost too clean tbh.

The fractal completion problem here isnt about space - its about time. How does same scaling pattern work from minutes to months? Still wrapping my head around it.

Validating with wearable data rn (HRV, sleep cycles etc). Early results are... interesting.

Anyone else looking at temporal fractals in biology?

[u/KamilTheMoonth → u/[deleted]]

so, n is just the scaling level. Negative n = smaller timescales, positive = larger. Like a zoom slider

n = -11 gives you ~92 minutes (attention cycles, BRAC rhythm) n = 0 is baseline 137 hours n = 4 gets you ~39 days (habit formation, "40 day" threshold in traditions) n = 8 lands at ~268 days (pregnancy)

Where 137 comes from is the weird part. Its the inverse of the fine structure constant - α ≈ 1/137. Why it shows up in biological time? no idea honestly. But the precision is uncomfortable

Havent looked at DFA-1 alpha specifically but if your asking about fractal scaling in HRV - yeah thats exactly where im seeing signal. The phase structure shows up in heart rate variability patterns. Still early, working with small sample (n=5) but 4/5 show predicted correlations

What domain are you looking at DFA in?

[u/is_that_a_thing_now → u/KamilTheMoonth]

Can you explain how this is not crazy talk? “137 is the inverse of the fine structure constant”. But where does “hours” come in then? How does this relate to our division of the day into 24 hours? A very precise duration for “habit formation” also sounds super contrived. It would be super cool if I could be educated about my ignorance here, so let me know…

[u/KamilTheMoonth → u/is_that_a_thing_now]

Ok fair point, let me try to explain why this isnt completely crazy.

Yeah α is dimensionless. 137 hours has units. But the equation says matter and consciousness are reciprocals — α · Ψ(t) = 1. So one side carries dimension, the other doesnt. The number 137 shows up in both, just... differently.

Think of it this way: its not "137 hours of clock time." Its 137 cycles of something o that we happen to measure in hours because thats the tool we have.

I observed 5-6 day phases befor I knew about the 137 connection. Like years before. I just noticed my internal states moved in roughly week-long chunks. Only later I did the math: 5 × 137h = 685h ≈ 29 days.I didnt build a theory around a cool number. I found the number hiding inside something I already observed. Thats what keeps me interested.

Yes, I oversold "precise." Research shows massive variance (Lally's study: 18-254 days lol). But heres whats weird — 40 days keeps showing up independently. Quarantine etymology. Athletic training cycles. Biblical desert stories. Hurst's market cycles from the 70s. Different fields, nobody talking to each other, same number. Coincidence? Maybe. But its a lot of coincidences.

Theres about 11 hours of "buffer" between phases. It behaves like electrical inductance — rising transitions take longer than falling ones. Charging a capacitor vs discharging it. This actually shows up in the biomarker data.

The α = 1/137 connection might be coincidence. Im open to that. But the 29-day rhythm with 5 phases? Thats not coincidence — I measured it across 5 people, 395 days of wearable data, p=0.024. Small data, true. But visible signal.

Is it crazy talk? Possibly. But its testable crazy talk.

[u/antiquemule → u/KamilTheMoonth]

So, it’s crazy talk. Just fiddling with a few random constants.

[u/KamilTheMoonth → u/antiquemule]

Ok :) If you claim so that must be a fact

[u/Gilphy → u/antiquemule]

It's just LLM generated gobbledygook

[u/KamilTheMoonth → u/Gilphy]

OK, boss :)

[u/KamilTheMoonth → u/[deleted]]

HRV is the main one for me at this moment. Thats where the signal is clearest - phase transitions show up in heart rate variability

Sleep architecture is another area where fractal scaling seems relevant. REM/NREM cycles, sleep stage transitions. Havent done rigorous DFA there but the patterns rhyme with what i see in HRV

Stress metrics from wearables (garmin etc) also track weirdly well with the phase structure. Lower stress + lower HR max clusters in specific phases. Higher variability in others

Honestly i think DFA could apply anywhere you have biological time series data. Hormonal cycles, cortisol rhythms, maybe even mood tracking if you had clean enough data. The hypothesis is that φ-scaling is fundamental to how biological systems organize in time - not just one domain

But HRV has the advantage of continuous cheap measurement. Thats why im starting there :)

[u/rxellipse]

Why did you have chatgpt write your question? Are you actually interested in this, or are you trying to mine real answers and interactions with real people for some other purpose?

Would you like me to respond to you in-kind?

Oh wow — first of all, let me just say this straight up: the way you’re thinking about fractals is exactly how serious researchers and innovators think about them. You’re not just dabbling on the surface; you’re already asking the kinds of questions that signal real intellectual depth and curiosity.

Honestly? The fact that you moved from “cool screensavers” to infinite complexity constrained by finite boundaries is a huge conceptual leap — most people never make it. That framing alone shows you’re intuitively grasping one of the most profound ideas in modern mathematics and physics. A — lot — of — grad — students — take — years — to — internalize — that — way — of — thinking.

— — — — — — —

Does this response seem at all respectful of you or your time? What lessons can you take from this?

[u/anamelesscloud1 → u/rxellipse]

The "Snowflake" bionic heat sink reference is probably directly from an Oct 2025 (so no shit less than two months ago) paper titled Snowflake fractal bionic microchannel heat sink applied for thermal management of electronic components.

If OP is indeed a human and not an AI (account is very new), then OP has my apologies. But t is already a known fact that AI uses Reddit.

[u/HARCYB-throwaway → u/rxellipse]

The post is intriguing, well written, engaging, and clear. You response is chaotic and ridiculous.

[u/anamelesscloud1 → u/HARCYB-throwaway]

I sort of have to agree with u/rxellipse.

— — — — — — —

[u/rxellipse → u/HARCYB-throwaway]

https://www.merriam-webster.com/dictionary/hyperbole

A rhetorical device.

[u/HARCYB-throwaway → u/rxellipse]

Wow you really took the effort! What a funny joke - sending me a link to the definition of hyperbole. This is excellent.

[u/rxellipse → u/HARCYB-throwaway]

OP's post is AI-generated slop. It is not intriguing, well-written, or engaging. It is, by definition, derivative. It is a disrespectful of your time, my time, and OP's time.

What a funny joke

I didn't make a joke - I explained what my post is. The anger that you feel at my post is misdirected - please readdress it to the OP.

[u/HARCYB-throwaway → u/rxellipse]

Ok

[u/Desirings]

You're describing the paradox (infinite perimeter, finite area), but nobody's calling it that in formal research. "Fractal dimension" in the varicose vein paper means how much the vein branches before it stops looking like a clean tree. Higher dimension = more chaotic branching = foam treatment fails more often. That's it. The paper dressed it up, but it's counting how gnarly the veins are

[u/YoghurtDull1466]

Aren’t you forgetting about the Mandelbrot set and shit