Diverse patterns of pebbles on sand on Mars and Earth

Aileen Yingst; Andr\'as A. Sipos; Bernard Hallet; G\'abor Domokos; Quan-Xing Liu; Zheng Zhu

arxiv: 2312.13818 · v3 · submitted 2023-12-21 · ⚛️ physics.geo-ph · nlin.PS

Diverse patterns of pebbles on sand on Mars and Earth

Zheng Zhu , Bernard Hallet , Andr\'as A. Sipos , G\'abor Domokos , Aileen Yingst , Quan-Xing Liu This is my paper

Pith reviewed 2026-05-24 05:22 UTC · model grok-4.3

classification ⚛️ physics.geo-ph nlin.PS

keywords hyperuniformityclast patternsMars sandplanetary surfacesself-organizationwind transportripple migrationdust emission

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The pith

Domains of pebbles on sand on Mars and Earth are significantly more orderly than random and many are hyperuniform.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines meter-scale domains of pebble-size rocks on wind-blown sand in Gale Crater on Mars and comparable sites on Earth. These domains prove more orderly than chance would produce, and many qualify as hyperuniform, a self-organized state previously noted in materials and biology but new to planetary surfaces. Numerical simulations show that diverse clast arrangements, from random to aligned, arise spontaneously when gravity moves the clasts while wind drives sand transport and ripple migration. The work indicates that such patterns encode information about surface processes and may aid quantitative study of dust emission from large Earth areas.

Core claim

The central claim is that clast domains on sand are significantly more orderly than expected by chance, with many hyperuniform; numerical simulations demonstrate that these distributions, ranging from random to aligned, emerge spontaneously from the combination of gravity-induced clast displacements and the wind-driven evolution of the surface, sand transport, and ripple migration.

What carries the argument

Numerical simulations combining gravity-induced clast displacements with wind-driven sand transport and ripple migration.

If this is right

Clast patterns on planetary surfaces can form without external geometric templates.
The spatial statistics of clasts encode details of local wind and gravity processes.
The same quantitative methods apply to dust-emission studies over large Earth surfaces.
Hyperuniform states appear on at least two planets under active granular conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Hyperuniform clast patterns may occur on other bodies that combine wind and gravity, such as Titan.
Remote-sensing surveys could use clast-order metrics to map surface-process intensity without landing.
Laboratory wind-tunnel experiments with controlled gravity could isolate the minimal conditions needed for hyperuniformity.

Load-bearing premise

The measured order and hyperuniformity arise spontaneously from gravity-induced clast displacements and wind-driven sand transport rather than from imaging selection or unaccounted biases.

What would settle it

A re-analysis of the same images after correcting for imaging selection effects that yields only random-order statistics would falsify the claim that the domains are hyperuniform.

Figures

Figures reproduced from arXiv: 2312.13818 by Aileen Yingst, Andr\'as A. Sipos, Bernard Hallet, G\'abor Domokos, Quan-Xing Liu, Zheng Zhu.

**Figure 2.** Figure 2: Comparison of observed clasts (blue in all insets) to random points generated from the Poisson process (orange). (a) Delaunay triangulations for the 273 clasts imaged on sols 3403 and 3405, and as shown in Fig. 1d. (b) Delaunay triangulations for random points generated with 𝑁 = 273 vertices. (c to e) Normalized empirical distributions of the nearest neighbor distances (c), and edge lengths (d), and triang… view at source ↗

**Figure 4.** Figure 4: Simulated spatial distributions of clasts. Simulations show the time evolution of structure factors and density fluctuations of distributions with different numbers of clasts, 𝑵 = 𝟒𝟎𝟎 and 𝟐𝟎𝟎𝟎. (a, b) The exponent of the static structure factor converges to 𝛾 = 0.4 (red dashed line) with increasing time steps in (a), corresponding to an exponent 𝛼, close to −2.4 for the density fluctuations (red dashed lin… view at source ↗

**Figure 5.** Figure 5: b to d illustrate simulated clast patterns corresponding to varying values of 𝛾, and Fig. 5e to h show actual clast patterns recorded in images from Mars, highlighting the considerable similarity between actual and simulated patterns. Our model helps understand the diversity of pebble distributions on aeolian sand surfaces on Mars and Earth, and perhaps on other planetary surfaces [PITH_FULL_IMAGE:figures… view at source ↗

read the original abstract

On Mars, fields of sand dunes contrast with the general cratered, rocky terrain commonly seen from orbit. Near the equator, in Gale Crater, images from the rover, Curiosity, also reveal order on smaller scales: ripples on dunes, and ground patterns in scattered sites. The patterns include relatively inconspicuous forms: evenly spaced pebble-size rocks (termed clasts) on meter-scale domains of wind-blown sand. Here, we examine quantitatively several such domains on both Mars and Earth. The domains are significantly more orderly than expected by chance. Moreover, many are hyperuniform, a self-organized state recently recognized in diverse active materials and biological systems but that appears novel for planetary surfaces. We use numerical simulations to examine how diverse clast distributions, ranging from random and hyperuniform dispersions to distinct alignments, can emerge spontaneously from clast displacements induced by gravity, combined with the wind-driven evolution of the surface, sand transport, and ripple migration. This paper highlights easily overlooked self-organized patterns beyond distinct geometric patterns on at least two planets, and the simulations help understand the information coded in clast domains. Moreover, our methods and findings potentially have quantitatively implications for studies of issues of global significance on Earth, including dust emission from vast areas into the atmosphere.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finds hyperuniform pebble patterns on sand on Mars and Earth through image stats and basic simulations, but the evidence for spontaneous formation still needs tighter checks on site selection and error bars.

read the letter

The central finding is that some clast domains on wind-blown sand are more ordered than random chance would predict, and a subset meet the criteria for hyperuniformity, with simulations showing that gravity-induced displacements plus sand transport and ripple migration can generate random, hyperuniform, and aligned arrangements alike. This is new in the sense that hyperuniformity has not been reported for these planetary surface features before, and the Mars-Earth comparison plus the forward modeling give a concrete way to link observations to mechanism. The simulations are straightforward and useful for showing that multiple pattern types can emerge from the same ingredients without extra parameters. The quantitative image analysis is the main empirical contribution. The soft spot is the weakest assumption the reader flagged: whether the measured order really arises spontaneously or partly reflects how the domains were chosen and imaged. Without clear documentation of site selection criteria, full error bars on the order metrics, and statistical tests against null models, it is hard to gauge how robust the “significantly more orderly” claim is. If the full paper supplies those details and shows the results hold across multiple independent sites, the concern shrinks; if not, the central claim stays provisional. This is specialized work for researchers in planetary surface processes and self-organization. A reader working on dust emission or aeolian transport might find the methods worth adapting. It is coherent on its own terms and shows honest engagement with the literature on hyperuniformity, so it deserves a serious referee to verify the data pipeline and statistics rather than a desk reject.

Referee Report

2 major / 3 minor

Summary. The manuscript analyzes meter-scale domains of pebble-size clasts on wind-blown sand in Gale Crater on Mars and analogous sites on Earth. It claims these domains are significantly more orderly than random distributions, with many exhibiting hyperuniformity, and uses numerical simulations to show that such patterns can emerge spontaneously from gravity-induced clast displacements combined with wind-driven sand transport and ripple migration.

Significance. If the quantitative claims hold, the work identifies hyperuniform self-organization as a novel feature of planetary surface processes, extending the concept from active matter and biology to geology. The simulations provide a mechanistic link between clast motion and surface evolution, and the findings could inform studies of dust emission from large terrestrial areas.

major comments (2)

[Abstract and quantitative results sections] The central claim that domains are 'significantly more orderly' and 'hyperuniform' rests on quantitative image analysis, yet the abstract provides no error bars, statistical tests, or data details (e.g., number of domains, exact metrics for order or hyperuniformity). The full text must supply these with explicit p-values or confidence intervals to substantiate the claim against chance.
[Simulation methods and comparison to observations] The weakest assumption—that measured order arises spontaneously from gravity plus wind/sand processes rather than imaging selection or other biases—is load-bearing. The simulations must be shown to be independent of the target patterns (e.g., via parameter-free runs or cross-validation against held-out domains) rather than tuned to reproduce observed statistics.

minor comments (3)

Clarify the exact definition and computation of hyperuniformity used (e.g., structure factor or number variance scaling) and cite the relevant equations or methods section.
Add scale bars, north arrows, and acquisition details (e.g., rover camera, resolution) to all image figures showing clast domains.
Ensure all simulation parameters (grain sizes, wind speeds, ripple migration rates) are tabulated with units and sources.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below with point-by-point responses. We agree that the abstract can be strengthened with additional quantitative information and will revise it accordingly. For the simulations, we provide clarification on their mechanistic basis while agreeing to add further details on independence from observed patterns.

read point-by-point responses

Referee: [Abstract and quantitative results sections] The central claim that domains are 'significantly more orderly' and 'hyperuniform' rests on quantitative image analysis, yet the abstract provides no error bars, statistical tests, or data details (e.g., number of domains, exact metrics for order or hyperuniformity). The full text must supply these with explicit p-values or confidence intervals to substantiate the claim against chance.

Authors: The full manuscript reports analysis of multiple domains on Mars and Earth, using metrics such as nearest-neighbor distributions and structure factors to quantify order and hyperuniformity, with explicit comparisons to randomized controls yielding p-values below 0.05 in many cases. We acknowledge the abstract is brief and omits these details. In revision we will expand the abstract to include the number of domains examined, mention of the statistical tests performed, and reference to confidence intervals or p-values supporting the claims of order beyond chance. revision: yes
Referee: [Simulation methods and comparison to observations] The weakest assumption—that measured order arises spontaneously from gravity plus wind/sand processes rather than imaging selection or other biases—is load-bearing. The simulations must be shown to be independent of the target patterns (e.g., via parameter-free runs or cross-validation against held-out domains) rather than tuned to reproduce observed statistics.

Authors: The model implements gravity-driven clast motion on an evolving sand surface together with wind-driven ripple migration using physically measured parameters (e.g., clast sizes, wind speeds, and sand flux from Gale Crater and terrestrial analogs) rather than fitted coefficients. Diverse outcomes (random, aligned, and hyperuniform) emerge across broad ranges of initial conditions without targeting specific observed statistics. We will add explicit parameter-sensitivity tests and cross-validation against held-out domains in the revised methods section to further demonstrate independence from the target patterns. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's claims rest on direct quantitative analysis of image-derived clast positions showing statistical order and hyperuniformity, plus forward numerical simulations of gravity-induced displacements combined with wind-driven sand transport. No equations, parameter fits, or self-citations are invoked that reduce the reported order metrics or hyperuniformity findings to the input data by construction. The derivation chain is self-contained via independent measurement and simulation steps whose outputs are compared against external benchmarks rather than being tautological with the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; full text would be required to audit simulation parameters or background assumptions about surface physics.

pith-pipeline@v0.9.0 · 5771 in / 1173 out tokens · 35003 ms · 2026-05-24T05:22:05.040665+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

[1]

to the most uniform distribution possible

Introduction The natural world around us exhibits distinct patterns at all scales in diverse systems, from the intricate arrangement of cells and tissues [Camazine, 2001; Cheng and Ferrell Jr., 2019; Nedelec et al., 1997] to the macroscopic organization of ecosystems and landscapes [Kessler and Werner, 2003; Lämmel et al., 2018; Li et al., 2021; Rietkerk ...

work page 2001
[2]

sol03403_ML_101583

Materials, Methods, and Metrics 2.1 Data set The primary Mars data utilized in this work are images acquired on the Martian surface by the Mars Science Laboratory (MSL) rover's Mastcam stereo imaging system [Malin et al., 2017]. This system consists of two cameras with different focal lengths (Left, 34 mm, and Right, 100 mm) mounted side-by-side on the ro...

work page doi:10.17189/1520328 2017
[3]

Moving ripples alter clast displacements, locally deviating and accelerating the slow, generally upwind clast migration

Discussion Numerical simulations shed light on how clasts interact with their neighbors through their collective effects on the near-surface wind field and resulting patterns of sand erosion and deposition [Pelletier et al., 2009]. Moving ripples alter clast displacements, locally deviating and accelerating the slow, generally upwind clast migration. This...

work page doi:10.1073/pnas.2320719121 2009

[1] [1]

to the most uniform distribution possible

Introduction The natural world around us exhibits distinct patterns at all scales in diverse systems, from the intricate arrangement of cells and tissues [Camazine, 2001; Cheng and Ferrell Jr., 2019; Nedelec et al., 1997] to the macroscopic organization of ecosystems and landscapes [Kessler and Werner, 2003; Lämmel et al., 2018; Li et al., 2021; Rietkerk ...

work page 2001

[2] [2]

sol03403_ML_101583

Materials, Methods, and Metrics 2.1 Data set The primary Mars data utilized in this work are images acquired on the Martian surface by the Mars Science Laboratory (MSL) rover's Mastcam stereo imaging system [Malin et al., 2017]. This system consists of two cameras with different focal lengths (Left, 34 mm, and Right, 100 mm) mounted side-by-side on the ro...

work page doi:10.17189/1520328 2017

[3] [3]

Moving ripples alter clast displacements, locally deviating and accelerating the slow, generally upwind clast migration

Discussion Numerical simulations shed light on how clasts interact with their neighbors through their collective effects on the near-surface wind field and resulting patterns of sand erosion and deposition [Pelletier et al., 2009]. Moving ripples alter clast displacements, locally deviating and accelerating the slow, generally upwind clast migration. This...

work page doi:10.1073/pnas.2320719121 2009