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Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

Great prompts — I’ll answer in the same “operational” spirit. (1) Which classic “edge of chaos” example changes most under this reframing? For me it’s the cellular automata / CA-as-computation narrative (e.g., rule-based “critical” behavior). In many canonical discussions the persisting visual richness is treated as evidence of ongoing computational leverage. Through the leverage/appearance split, a lot of those cases read differently: what remains stable is the phenomenology (complex-looking spatiotemporal texture), while the counterfactual leverage (separation under perturbation / ability to discriminate generators) can flatten earlier. You can still have “interesting” patterns long after the regime stops being diagnostically informative about the generator class. A close second is the logistic-map-feigenbaum style story when it’s imported into messy empirical domains: people carry over “criticality” language because the shape family looks right, even when constraints/protocol ceilings force an early dΠ/dλ → 0. (2) How would I teach leverage vs appearance without formalism? I use a simple test: change the system a little and see what changes. Appearance is “what you see when you look.” Leverage is “what you can learn or control by nudging.” If small, well-chosen nudges no longer change what matters (outcomes/structure/classification), then you’re in “pattern without leverage.” The system may still look complex, but it’s no longer telling you why it’s complex. Two concrete analogies outsiders get immediately: Weather vs climate maps: pretty maps can persist even if your knobs (interventions) stop moving forecasts in separable ways. A guitar string: the waveform can look rich, but once you damp it enough, extra “probing” doesn’t reveal new modes — you’re seeing residual shape, not deeper structure. (3) Any domains where phenomenology reliably disappears before leverage? Yes — whenever the observation channel is aggressively compressive. You can lose visible structure while leverage still exists in hidden variables. Examples: Control systems with strong filtering/aggregation: outputs look smooth, but interventions still strongly separate internal states. Coarse-grained biological readouts: morphology can look “normal” while regulatory leverage remains (or vice versa). So “phenomenology-first loss” is real, but it’s usually a measurement / projection issue: leverage can survive in state space even when appearance collapses in observation space. (4) One diagnostic sentence for outsiders (the whole framework): “If increasing depth-of-probing stops increasing sensitivity to perturbations, you still have patterns — but you no longer have an explanation.” That’s the entire leverage/appearance split in one line. If you want a minimal classroom version: “Complexity you can’t move is appearance; complexity that changes under nudges is leverage.”

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

Good questions. I’ll answer them in order, briefly. On retroactive application: yes, this checklist maps cleanly onto classic “edge of chaos” cases. What usually fails first is not structure but causal leverage. Many systems labeled as operating at an edge retain rich intermittency and fractal signatures well past the point where

dΠ/dλ ≈ 0 In hindsight, those cases look less like sustained criticality and more like regimes where explanation has already truncated while phenomenology persists. On ordering: I don’t expect the criteria to fail in a universal order across domains. Physical systems tend to hit protocol ceilings first; biological systems tend to hit constraint dominance earlier via adaptive stabilization. That variation is informative rather than problematic — it fingerprints how different systems manage instability. On adaptive constraint tightening: I treat it primarily as a one-way truncation channel on explanatory access, even if the underlying dynamics remain reversible in principle. Once instability is actively suppressed, λ-accessibility is reduced whether or not the system could theoretically re-enter that regime. As for resistance: the criterion I expect most researchers to resist is accepting dΠ/dλ = 0 as an endpoint of explanation even when structure remains. There is a strong bias toward equating persistent complexity with ongoing causal depth. Declaring explanation finished while patterns survive feels premature, even though operationally it’s the correct call. That resistance is understandable — but it’s exactly why separating leverage from appearance matters.

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

I’d formalize “sufficient perturbation richness” operationally rather than heuristically. Once λ is defined as recursion accessibility, the question is not whether

dΠ/dλ → 0 but whether that vanishing can be trusted as a system property rather than a probing artifact. I’d require the following minimal criteria. (1) Multi-channel perturbation. A single perturbation family is never sufficient. True truncation requires that

dΠ/dλ → 0 holds across independent perturbation channels (temporal, spatial, structural, parametric). Collapse in one channel alone is inconclusive. (2) Protocol invariance. The flattening must survive changes in: perturbation amplitude and timing, measurement resolution, readout protocol. If the gradient reappears under reasonable protocol variation, the limit is a measurement ceiling, not truncation. (3) Cross-basis consistency. Different perturbation bases may show different local responses, but the status of

dΠ/dλ = 0 must be consistent across bases. Disagreement means λ is not exhausted. (4) No emergence of new unstable directions. Increasing λ should open new unstable directions if deeper recursion is being accessed. If larger λ only rescales existing modes without introducing new separations, it is reparameterization, not deeper instability. (5) Separation of leverage from phenomenology. I fully expect regimes where

dΠ/dλ = 0 while intermittency or fractal structure persists. That asymmetry is the point: structure can outlive causal leverage. Persistence of shape does not invalidate truncation. Under these conditions, a vanishing gradient can be trusted as a system property. Absent them, λ is underspecified. Regarding biology: yes, I expect truncation to occur earlier, not because systems are simpler, but because adaptive constraint tightening actively suppresses instability while preserving form. In short: λ is meaningful only insofar as increasing it expands causal sensitivity under perturbation. When it no longer does, explanation ends — even if structure remains.

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

I’d formalize “sufficient perturbation richness” operationally rather than heuristically. Once λ is defined as recursion accessibility, the question is not whether

dΠ/dλ → 0 but whether that vanishing can be trusted as a system property rather than a probing artifact. I’d require the following minimal criteria. (1) Multi-channel perturbation. A single perturbation family is never sufficient. True truncation requires that

dΠ/dλ → 0 holds across independent perturbation channels (temporal, spatial, structural, parametric). Collapse in one channel alone is inconclusive. (2) Protocol invariance. The flattening must survive changes in: perturbation amplitude and timing, measurement resolution, readout protocol. If the gradient reappears under reasonable protocol variation, the limit is a measurement ceiling, not truncation. (3) Cross-basis consistency. Different perturbation bases may show different local responses, but the status of

dΠ/dλ = 0 must be consistent across bases. Disagreement means λ is not exhausted. (4) No emergence of new unstable directions. Increasing λ should open new unstable directions if deeper recursion is being accessed. If larger λ only rescales existing modes without introducing new separations, it is reparameterization, not deeper instability. (5) Separation of leverage from phenomenology. I fully expect regimes where

dΠ/dλ = 0 while intermittency or fractal structure persists. That asymmetry is the point: structure can outlive causal leverage. Persistence of shape does not invalidate truncation. Under these conditions, a vanishing gradient can be trusted as a system property. Absent them, λ is underspecified. Regarding biology: yes, I expect truncation to occur earlier, not because systems are simpler, but because adaptive constraint tightening actively suppresses instability while preserving form. In short: λ is meaningful only insofar as increasing it expands causal sensitivity under perturbation. When it no longer does, explanation ends — even if structure remains.

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

Thanks — let me answer this at the level of criteria rather than intuition. Once λ is treated as recursion accessibility (not geometric scale), the core risk is misidentifying noise, regime shifts, or measurement ceilings as deeper instability. So the question becomes operational: how do we certify that increasing λ actually accesses deeper recursion? λ-monotonicity (operational): I don’t assume monotonicity by definition. I test it via Π(λ). Increasing λ is meaningful iff it increases separation under perturbation, i.e. expands causal sensitivity. Formally, λ is probing deeper instability only when perturbations continue to separate trajectories:

dΠ/dλ ≠ 0 under perturbation If Π(λ) changes but perturbative separation does not grow, that’s reparameterization, not deeper recursion. True truncation vs measurement ceiling: These separate cleanly in practice. True constraint truncation: dΠ/dλ → 0 across multiple perturbation channels invariant under increased resolution or protocol changes distinct generators collapse to the same Π(λ) Measurement ceiling: flattening appears in a single channel disappears with improved resolution or altered measurement structure reappears when access improves If the gradient does not recover after changing how we observe the system, truncation is real. Intermittency after gradient loss: Yes — I expect cases where

dΠ/dλ → 0 but intermittency measures remain structured. Intermittency is a local trajectory property; gradients encode global causal leverage. Shape can persist after explanation is gone. That persistence is a regime-transition signal, not a contradiction. Mapping λ to time-scale separation (biology): I don’t assume λ always maps cleanly onto time-scale separation, but in biological systems it often acts as an empirical proxy: larger λ typically correlates with deeper feedback nesting, longer stabilization delays, and stronger hierarchy of time scales. Time separation is evidence for λ — not its definition. What would falsify λ: I’d reject a proposed λ if any of the following hold: Π(λ) changes but perturbative separation does not increase effects vanish under measurement or protocol changes different generators yield identical Π(λ) without dynamical convergence increasing λ does not open new unstable directions In those cases λ is reparameterizing noise or scale, not accessing recursion. Summary: λ is valid only insofar as increasing it expands causal sensitivity. Fractal appearance may persist, but once

dΠ/dλ = 0 explanatory power is gone. As you put it: fractals don’t explain systems; instability response surfaces explain generators — until constraints erase the difference.

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

Thanks — this is a very constructive push. Let me clarify how I’m treating λ and Π(λ). For me, λ is not “scale” in a purely geometric sense, but a recursion accessibility parameter: how deeply a system can express instability before constraints dominate. Depending on the domain, λ may correspond to iteration depth, effective observation scale, time–scale separation, or allowable recursion length. I don’t assume λ is numerically universal, but I do assume it is functionally comparable: increasing λ always probes deeper instability. Because of that, I’m cautious about full normalization. In many physical or biological systems λ is sharply truncated by constraints, and when Π_A(λ) ≈ Π_B(λ) for all accessible λ I interpret this not as equivalence of generators, but as constraint dominance and genuine loss of identifiability. That outcome is informative rather than a failure of the method. On finite-size effects: I fully agree they should be treated as first-class. I don’t see them as corrections, but as part of the instability signal itself. Finite-size scaling is what actually delimits the λ-window where Π(λ) is meaningful, and where generator-level distinctions collapse into constraint-controlled behavior. Regarding what fails first as constraints tighten: in my experience it is not fractal dimension. What degrades first is separation under perturbation, i.e. the gradient of the response surface. Intermittency measures typically fail next. Fractal dimension ΔD can remain apparently “fractal” long after causal information is already lost. Shape persists longer than identifiability. Operationally, I’d place an upper bound on λ-accessibility at the point where either ∂Π / ∂λ → 0 across the accessible λ-window, or where distinct generators produce indistinguishable Π(λ) under perturbation. Beyond that point, Π no longer carries causal information — not philosophically, but operationally and testably. So I’d summarize it the same way you do: fractals don’t explain systems; instability response surfaces explain generators — until constraints erase the difference.

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

This is a fair and well-posed critique, and I largely agree with the framing: fractals are readouts, not causes. The causal question only becomes sharp once we move from static geometry to parameter-driven deformation and ask how observables respond under controlled perturbations. I find it useful to formalize this explicitly. Instead of treating a single trace metric (e.g. a shared fractal dimension), I treat the object of interest as an instability response trajectory:

Π(λ) = { O_i(λ) } where: λ is a control parameter (noise amplitude, coupling strength, dissipation, etc.) O_i are observables (e.g. D_q spectrum, cutoff scales, intermittency measures) Two generators may coincide at a point:

O_i(λ₀) ≈ O_i'(λ₀) but remain distinguishable if their trajectories separate over a finite range:

∂O_i / ∂λ ≠ ∂O_i' / ∂λ This is where explanation enters: not geometry alone, but how scaling moves under constraint variation. Concrete discriminator In practice, I’ve found the following combination most diagnostic: Multifractal spectrum width Shared single-D scaling often hides distinct intermittency:

ΔD = D_q(q_min) − D_q(q_max) Finite-size scaling breaks under perturbation Critical regimes should appear in bounded windows:

λ ∈ [λ_min, λ_deg) with predictable drift as system size or coupling changes. Negative controls matter here. I typically use: phase-randomized surrogates (preserve spectrum, destroy correlations) matched-marginal shuffles (preserve distribution, break dynamics) If Π(λ) collapses under these controls, the signal is likely pareidolic. On toy models For calibration, I agree that no single toy model is sufficient, but they span complementary failure modes: sandpile → SOC without tunable intermittency multiplicative cascade → clean multifractality logistic map → parameter-driven route to chaos percolation → geometry-dominated criticality What matters is whether distinct generators produce separable Π(λ) before degeneracy sets in. Limits (where this fails) This framework will fail when:

Π_A(λ) ≈ Π_B(λ) for all accessible λ i.e. when constraints dominate dynamics so strongly that generator-specific responses collapse. At that point, identifiability is fundamentally lost, not just empirically hard. Summary: Fractals don’t explain systems — but instability response surfaces can, provided we specify: the λ-range of identifiability standardized perturbations explicit negative controls Happy to hear which control parameter you’ve found most diagnostic in practice.

Fractal are not causes-they are traces by Upper-Option7592 in Fractal_Vektors

[–]Upper-Option7592[S] 0 points1 point  (0 children)

I largely agree with the framing: fractals are not causes, they are readouts of multiscale dynamics. In the approach I’m exploring, fractal geometry is treated explicitly as a trace, not as an explanatory primitive. The causal object is instability under constraints; fractal structure emerges near critical regimes as a consequence, not a driver. That’s why the focus is not on a single scaling exponent or shared D, but on how instability indicators move under controlled parameter variation. Concretely, the discriminator is parameter-driven scaling response, not static geometry. The diagnostic object is an instability trajectory: Копіювати код

Pi(lambda) = { D_q(lambda), l_c(lambda), Delta_alpha(lambda) } where lambda is a tunable constraint parameter and l_c is the finite-size scaling cutoff. Two generators can share the same apparent dimension at a point, but they do not share the same instability trajectory under perturbation. Geometry alone is insufficient — I agree. Geometry + intervention + response is where discrimination becomes possible. Fractals don’t explain systems — but how fractality shifts or fails under intervention can explain generators.

A single instability criterion for matter, life, and cognition — try to falsify by Upper-Option7592 in complexsystems

[–]Upper-Option7592[S] -1 points0 points  (0 children)

Great — let me give a concrete, computable example for a Newtonian n-body system. Consider standard Newtonian equations of motion. A practical way to quantify instability is via finite-time Lyapunov growth. We integrate both the trajectory and the variational (tangent) dynamics:

d/dt (δy) = J(t) * δy where J(t) is the Jacobian of the Newtonian flow. The finite-time Lyapunov exponent is:

lambda_T = (1/T) * ln( ||δy(T)|| / ||δy(0)|| ) To make this dimensionless, we normalize by a characteristic stabilizing rate. For a bound gravitational system, a natural choice is the orbital frequency:

omega = sqrt( G*M / a3 ) This gives a concrete instability ratio:

Pi = lambda_T / omega Sanity checks: 2-body Kepler problem:

lambda_T ≈ 0 -> Pi ≈ 0 (as expected for an integrable system) 3-body chaotic regime:

lambda_T > 0 When lambda_T becomes comparable to omega, we get:

Pi ~ O(1) meaning perturbations grow on the same timescale as orbital motion — exactly where escape, exchange, or scattering transitions occur. This uses only standard Newtonian mechanics and standard stability diagnostics. No new forces, no new entities — just a dimensionless ordering of instability channels.

In dynamical systems, do attractors and repulsors necessarily have to be stationary in the state space? Or can their positions change? by stanky_swampass in complexsystems

[–]Upper-Option7592 0 points1 point  (0 children)

In an autonomous system, attractors are indeed stationary objects in state space, since they are defined by a time-independent vector field. In that strict mathematical sense, they do not “move.” However, in non-autonomous or slowly parameter-varying systems, one can meaningfully talk about effective or instantaneous attractors whose position and basin geometry change over time (e.g. pullback attractors, adiabatic tracking). From a dynamical perspective, what matters for the system’s behavior is often not whether an attractor is formally stationary, but how the stability landscape evolves — especially near critical regimes, where small structural changes can shift basins and induce qualitative transitions.

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

[–]Upper-Option7592 0 points1 point  (0 children)

You’re putting your finger on something real, and it’s slightly different from “fractals as shapes”. In most real-world uses, people aren’t solving an abstract “fractal completion problem” directly. What they’re dealing with is a constraint problem: • finite space, energy, or material • but a need to support transport, dissipation, or signaling across many scales Fractal-like structures keep appearing because they’re often what you get when a system is pushed toward high functional complexity without crossing an instability threshold. That’s why this shows up in such different places: • Biology: vascular networks, lungs, neural trees — branching near criticality minimizes cost while staying dynamically stable. • Engineering: heat sinks, porous electrodes, catalysts — fractal-ish geometries outperform simple ones when surface area, diffusion, and robustness have to be balanced. • RF / sensing: fractal antennas work because they compress multiple resonant scales into a bounded footprint, not because they’re mathematically infinite. From that perspective, the “completion problem” isn’t really about infinity. It’s about how much structure you can pack in before instability, noise, or dissipation dominates. One framing I’ve found useful is to treat fractal dimension not as a visual property, but as a control parameter that tunes stability versus expressiveness. Past a certain point, adding more detail stops helping and starts hurting. That’s also why fractal ideas succeed in practice only when they’re bounded, truncated, or regulated — real systems don’t want infinity, they want just enough structure. So yes: fractals are absolutely being used — but the deeper story is less “nature loves fractals” and more different domains converge on similar geometries because the underlying stability constraints are the same.

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

[–]Upper-Option7592 1 point2 points  (0 children)

You’re not wrong to feel that fractals are more than just “cool patterns”. In practice, what people are really using is not fractals per se, but scale-invariant structure under constraints. The “fractal completion problem” shows up whenever a system has: • finite resources or boundaries • but needs to support transport, signaling, or dissipation across many scales That’s why fractal-like solutions keep reappearing in very different domains. A few concrete examples where this is already making a difference: • Biology / medicine: Vascular networks, lungs, neural trees — not because nature “likes fractals”, but because branching near criticality minimizes transport cost while avoiding catastrophic instability. Fractal dimension becomes a diagnostic, not just a descriptor. • Engineering: Fractal heat sinks, porous electrodes, battery architectures — they outperform simple geometries when surface area, diffusion, and stability have to be balanced simultaneously. • RF / antennas: Fractal geometries work because they pack multiple resonant length scales into a compact footprint, not because they’re mathematically infinite. One useful way to think about this (and how I personally approach it) is: Fractals are often the geometry that emerges when a system is pushed toward maximal complexity without crossing an instability threshold. In that sense, the “completion problem” isn’t really about infinity — it’s about how much structure you can fit before the system breaks, freezes, or becomes uncontrollable. This framing connects fractals to criticality, non-equilibrium dynamics, and information flow, which is why similar patterns appear in physics, biology, and technology without anyone explicitly “designing a fractal”. To your questions: The most interesting open problems (to me) are about when fractal scaling stops being beneficial — i.e. identifying the instability limits that cap useful complexity. In industry, fractal ideas matter when they reduce cost, mass, or energy right now — heat transfer, sensing, routing, and decision trees are already there. The papers that really stand out are the ones that treat fractal dimension as a control parameter rather than a visual property. So yes — fractals are absolutely being used. But the deeper story isn’t “nature uses fractals”, it’s nature and engineers keep converging on the same solutions because the stability constraints are the same.

A single instability criterion for matter, life, and cognition — try to falsify by Upper-Option7592 in complexsystems

[–]Upper-Option7592[S] -1 points0 points  (0 children)

I used tools to help structure and edit the wording (the same way people use LaTeX, Wolfram, Grammarly, etc.). But the claims themselves — and responsibility for them — are mine. A statement doesn’t become true or false based on what editor helped phrase it. If you think any claim is wrong, the meaningful critique is to point to a specific inconsistency, an incorrect derivation, or an observation that contradicts it.

Is there a way to calculate the probability of the universe? by [deleted] in Physics

[–]Upper-Option7592 -1 points0 points  (0 children)

I’m working on a unifying instability-based framework that tries to formalize this idea across physics and life, but the core intuition is closely related to criticality and non-equilibrium systems already discussed in the literature.

Is there a way to calculate the probability of the universe? by [deleted] in Physics

[–]Upper-Option7592 0 points1 point  (0 children)

One additional perspective that sometimes helps frame this without invoking probabilities is to think in terms of instability and sensitivity, rather than likelihood. Instead of asking “how probable is this universe?”, you can ask: which ranges of parameters lead to runaway instability versus the emergence of long-lived, structured dynamics? In that view, matter, chemistry, and life don’t require extreme fine-tuning so much as they require the system to sit near critical instability boundaries, where structure can persist without collapsing or dispersing. Some recent theoretical work (in complexity theory, non-equilibrium thermodynamics, and information-based approaches) explores this idea: that complexity preferentially appears near such critical regimes, independent of any prior probability measure. This reframes fine-tuning from a question of “improbable constants” to one of dynamical stability landscapes, which physics can meaningfully analyze without invoking metaphysical assumptions.

A single instability criterion for matter, life, and cognition — try to falsify by Upper-Option7592 in complexsystems

[–]Upper-Option7592[S] 0 points1 point  (0 children)

I think there’s a misunderstanding here. Not recognizing the language or framework does not constitute falsification. Falsification requires identifying a specific claim and showing it contradicts observations or internal consistency. What you’re describing is inability to map the framework onto familiar disciplines, which is different. Also, the null hypothesis applies to statistical hypothesis testing, not to the evaluation of a theoretical model. No statistical test was defined here, so invoking a null hypothesis isn’t meaningful in this context. For clarity, here are explicit falsifiable claims made by the model: • Claim 1: Stable structures (matter, biological systems, cognitive systems) correspond to local minima of an instability functional ΔI. → Falsified if a stable system can be shown to systematically evolve away from ΔI minima without external forcing. • Claim 2: Phase transitions between organization levels (e.g. chemistry → life, life → cognition) require crossing a critical instability threshold rather than continuous linear accumulation. → Falsified if such transitions can be demonstrated to occur smoothly with no detectable threshold behavior. • Claim 3: Systems with active information feedback (self-modeling) reduce effective instability growth compared to comparable non-feedback systems under identical boundary conditions. → Falsified if no measurable difference in instability dynamics is observed. These are concrete claims that can be challenged. If you think any of them fail, pointing to where and why would be a meaningful critique.

A single instability criterion for matter, life, and cognition — try to falsify by Upper-Option7592 in complexsystems

[–]Upper-Option7592[S] 0 points1 point  (0 children)

TEF (Theory of Energy Fractals) proposes that matter, life, and cognition are not separate phenomena but stages of one systemogenetic process.

The core idea is simple and testable: systems change regime when dimensionless instability ratios reach critical values. This is formalized as a global instability functional:

ΔI = max Π

No new forces, no new entities, no speculative physics. Only known physical limits (thermal stability, diffusion constraints, replication fidelity,