ICICLE: Multidisciplinary Insights

• ICICLE is a multidisciplinary term encompassing hierarchical visualization techniques, continual learning models, scalable data monitoring systems, and natural ice growth studies.
• Key applications include icicle plots for hierarchical data display, biomedical analytics, temporal healthcare analytics, and firmware fuzzing across various architectures.
• Research on natural icicles informs our understanding of ice growth instabilities and ripple formation, while programmable-matter 'icicles' inspire algorithmic construction in robotics and soft-matter physics.

Across the cited literature, ICICLE denotes several unrelated objects. In visualization research it denotes the icicle plot, a hierarchical layout for quantitative trees; in machine learning and systems it names methods and platforms including Interpretable Class-InCremental LEarning, In-Context Indexing for doC-Level Expansion, a multi-architecture emulator for grey-box firmware fuzzing, an NSF AI institute for Intelligent CyberInfrastructure with Computational Learning in the Environment, and a metadata indexing and monitoring framework for HPC file systems. In physics, materials, and morphology research, icicle remains the natural ice form whose growth, ripple instability, and internal inclusions are studied experimentally and theoretically [1908.01277] [2303.07811] [2605.26902] [2301.13346] [2304.11086] [2604.10295] [1301.4734].

1. Icicle plots as a hierarchical visual encoding

In the visualization literature, an icicle plot is a hierarchical visualization in which hierarchy is shown by stacked layers, parent nodes occupy a band, children are laid out beneath them, and quantitative value is encoded by length rather than area or angle. It is a “top-down” hierarchical layout with juxtaposed layers representing tree depth. The format was originally developed for hierarchical clustering and has more recently been used in designs such as SyncTRACE and Flame Graphs [1908.01277].

A central comparative study evaluated treemaps, icicle plots, sunburst charts, and a semicircular variant called the sundown chart. In a pilot study with 6 participants, the sunburst chart was least preferred and was therefore dropped from the main study. In the controlled study with 12 participants, the icicle plot, sundown chart, and treemap were compared under a shared interaction framework including overview + detail, zoom and pan, drill-down, roll-up, breadcrumb-like context, and a scale for size comparison. On Q1 – Navigate to a specific node, the icicle plot averaged 32.6 s, the sundown chart 35.2 s, and the treemap 53.0 s; on Q3 – Identify the closest relationship between Node A and Node B, the corresponding times were 20.0 s, 20.6 s, and 44.2 s; on Q4 – What is the least common ancestor of Node A and Node B, the icicle plot averaged 20.3 s, compared with 25.8 s for the sundown chart and 33.0 s for the treemap. For Q3, accuracy was 97.2% for both the icicle plot and sundown chart, versus 91.4% for the treemap. Participants described the icicle plot as intuitive and easy to learn, and overall preference slightly favored the icicle plot [1908.01277].

The same literature also positions the icicle plot within a larger design space. A treemap uses area and containment to show hierarchy but can suffer from unstable layout, awkward aspect ratios, harder navigation in large hierarchies, and more difficult value comparison. A sunburst chart is a radial version of the icicle plot using angle to represent quantitative value, while the sundown chart is a semi-circular radial hybrid intended to suit the 16:9 aspect ratio of modern monitors while retaining some radial benefits [1908.01277].

The Radial Icicle Tree (RIT) extends this family by transforming the rectangular bounding box of an icicle tree into a circle, circular sector, or annular sector while introducing gaps between nodes and maintaining area constancy for nodes of the same size. Its stated purpose is to address three problems: in standard icicle trees, some rectangles are too narrow to notice easily; in sunburst trees, equal values can appear with different areas at different depths; and in both representations, nodes from different subtrees can visually merge. RIT therefore preserves faithful area encoding while adding explicit node separation [2307.10481].

2. Biomedical, temporal, and ontology-centered uses of icicle visualizations

A prominent biomedical use appears in EMAGE, the eMouse Atlas of Gene Expression. EMAGE stores in situ gene-expression results in a large hierarchical anatomy space with up to 26 Theiler Stages (TS), roughly 2000 anatomical structures in later stages, and up to about 19,000 genes expressed in a stage. The icicle diagram was introduced because tabular annotations and grouped heat maps were useful for search but weak for interactive browsing, overview, and anatomical navigation. In this setting, the icicle is described as essentially a linear sunburst: the root node representing the mouse is at the top, child structures are laid out beneath it, and the visualization uses the partOf tree subset of the EMAP anatomy rather than the full DAG. Nodes encode expression status by color using the EMAGE scheme—strong red, moderate yellow, weak purple, not detected cyan, propagated pink, and no expression information grey—and node size is tied to the number of descendants. Positive expression is propagated upward along the partOf chain, so if a gene is expressed in the digit, then also in the paw, and therefore also in the limb; propagated expression is shown in pink, while negative expression is not propagated. The implementation used d3.js and Django/Python, supported hover, query refinement, stage navigation, and click-to-zoom, and the evaluation reported that the sunburst was the more popular visualization overall, but the icicle achieved higher SUS usability scores and its zoom functioned perfectly even at large stages where sunburst zoom became unreliable above roughly TS14 [1407.2117].

In temporal healthcare analytics, ParcoursVis uses an Icicle tree as the main overview for aggregated electronic health record sequences. The system incrementally processes patients in chunks, updates an aggregated prefix tree, and renders the partial result immediately rather than waiting for full ingestion. In that view, node height encodes frequency, node width encodes average (or median) duration, time flows from left to right, and siblings are sorted vertically by frequency. Because frequency-based resorting can cause flicker, ParcoursVis introduces Hysteresis Sort, preserving previous order when adjacent nodes have nearly equal frequency. The paper formalizes the inertia threshold with
$$
\forall {i, j}, i<j \implies freq(child_j)-freq(child_i) \le \epsilon
$$
and chooses a default inertia of about (20/1080 \approx 0.02), corresponding to roughly 20 pixels at the top level on a 1080p display. The system reports support for 10 million patients in the demonstrated dataset and claims support for more than 100 million patients; for a 250k chunk size on 6 threads, the best reported progressive configuration yields about 19.8 ms per iteration median. In the stability evaluation, the tree became stable after roughly 80% of the dataset had been processed at depth 4 with Hysteresis Sort, compared with about 90% for regular sorting [2508.10700].

A different use appears in selection-bias analysis for high-dimensional medical cohorts. Integrated into Cadence, the proposed workflow distinguishes a baseline cohort from a focus cohort and compares them using a provenance tree, cohort overlap view, hierarchical dot plot, list view, variable distribution view, and a novel split icicle plot. Distributional shift is quantified with Hellinger distance,
$$
H(P,Q) = \sqrt{\frac{1}{2}\sum_{i=1}^{n}(\sqrt{p_i}-\sqrt{q_i})^2},
$$
and summarized over all (m) dimensions as
$$
H_{avg}(c_i,c_j)=\frac{1}{m}\sum_{k=1}^{m}H(d_{ik},d_{jk}).
$$
The split icicle plot uses a three-stage algorithm—Split, Sort, Merge—and encodes drift with a grey-red map, black outlines for salient nodes, a diamond symbol (\blacklozenge) for constrained nodes, dashed split markers, and reduced-height groups for non-salient merged regions. In the paper’s example, the detailed comparison revealed that the focus cohort had 59% incidence of Sleep apnea (133 of 227) versus 29% in the baseline (496 of 1,732) [1906.07625].

Ontology visualization provides a fourth applied variant. OntoPlot retains an ontology’s subsumption hierarchy as an icicle-plot-like hierarchical layout, but modifies standard icicles by using circle glyphs within boxes and by wrapping leaf children into larger boxes to reduce width. The system compresses leaf nodes, chains, and subtrees into distinct glyphs, supports search, focus mode, and expand/collapse interaction, and highlights classes involved in a selected association type using color and label emphasis. In the expert evaluation with 12 participants, OntoPlot was significantly faster on association-oriented tasks such as T7, T8, T9, and T10, and for G2 and G3 tasks all participants preferred OntoPlot over the ontology editor [1908.00688].

3. ICICLE in continual learning and retrieval

In machine learning, ICICLE may denote Interpretable Class-InCremental LEarning, an exemplar-free continual-learning method built for prototypical part-based concept models. The method addresses interpretability concept drift, the case in which the model’s concept visualizations or similarity maps change across incremental tasks even when predictive accuracy remains acceptable. ICICLE introduces three mechanisms: interpretability regularization that distills previously learned concepts while preserving positive reasoning, a proximity-based prototype initialization strategy for the fine-grained setting, and task-recency bias compensation for prototypical parts. It uses task-specific prototype layers (g^t) and final layers (h^t), removes the negative weights of the original ProtoPNet last layer, and defines an interpretability-drift measure
$$
ICD = \mathbb{E}{i,j=1}^{H,W}\left|sim(p^{t-1}, z{i,j}^{t}) - sim(p^{t}, z_{i,j}^{t})\right|.
$$
On CUB-200-2011, task-aware accuracy for 4 / 10 / 20 tasks was reported as 0.654 / 0.602 / 0.497 for ICICLE, compared with 0.560 / 0.531 / 0.452 for Freezing and 0.445 / 0.288 / 0.188 for EWC; task-agnostic accuracy was 0.350 / 0.185 / 0.099. On Stanford Cars, task-aware accuracy was 0.654 / 0.645 / 0.583, and task-agnostic accuracy was 0.335 / 0.203 / 0.116. In the IoU-based stability analysis of prototype similarity maps, ICICLE achieved mean IoU 0.728, versus 0.151 for Finetuning, 0.334 for EWC, 0.188 for LWF, and 0.325 for LWM [2303.07811].

In retrieval, ICICLE may instead denote In-Context Indexing for doC-Level Expansion, a framework for extending generative retrieval to newly added documents at inference time without retraining on the expanded corpus. The method treats incremental corpus growth as an in-context retrieval problem by supplying document–docid pairs in the prompt and teaching the model to distinguish context-grounded retrieval from parametric retrieval. The central routing mechanism is a special token, ([COPY]), with target defined as
$$
\tilde{y}i =
\begin{cases}
[COPY]\; y^*, & \text{if } y^* \in \mathcal{Y}(\mathcal{C}),\
y^*, & \text{otherwise}.
\end{cases}
$$
If the model emits ([COPY]), decoding is constrained by a trie built over context-provided docids; otherwise it decodes from the global corpus trie. ICICLE combines this with Direct Preference Optimization (DPO) and large title context adaptation. On MS MARCO, it reports Hits@1 = 0.607 and Hits@10 = 0.800 for newly added documents; on NQ320K, Hits@1 = 0.649 and Hits@10 = 0.772. The ablation study shows that adding ([COPY]) raises Hits@1 on (\mathcal{D}{\text{new}}) from 0.102 to 0.526, DPO raises Hits@1 on (\mathcal{D}_{\text{train}}) from 0.379 to 0.549, and large-context adaptation further improves unseen-document retrieval. The analysis reports that high-shot degradation is mainly due to routing failure, while conditional retrieval accuracy (P(\text{hit}\mid [COPY])) remains around 0.943 to 1.000 [2605.26902].

These two uses share the acronym but are otherwise unrelated. One concerns class-incremental continual learning and explanation stability; the other concerns incremental generative retrieval and docid generation.

4. ICICLE as cyberinfrastructure and large-scale data infrastructure

One uppercase usage refers to the NSF-funded Artificial Intelligence Institute for Intelligent Cyberinfrastructure with Computational Learning in the Environment. A student-led software report describes efforts to make ICICLE resources accessible through authenticated Jupyter Notebooks and Python command line clients. The workflow is built around TACC usernames and passwords, the Tapis Tokens API, a returned JWT access token, and access to Tapis Pods and other Tapis-managed services. The report uses Neo4j to organize data into a knowledge graph, hosts the graph on a Tapis Pod, and connects to it with Py2Neo. It describes two CLIs—TapisCL-ICICLE and ICICONSOLE—as well as a neural-network notebook for classifying asteroids as hazardous or harmless, reporting about 75% accuracy and 3.8% false negatives [2304.11086].

A later ICICLE paper treats the institute as the operational substrate for dynamic model governance. In that work, Patra Model Cards are embedded in the ICICLE ecosystem, alongside Tapis, ML Field Planner / MLFieldPlanner, TapisUI, MLProvisioner, MLEdgeServer, and CKN. Model cards are treated as dynamic objects rather than one-time training artifacts, and the evaluation compares REST against two MCP implementations: a native MCP server talking directly to Neo4j and a layered MCP server wrapping REST. For a few-KB model card, end-to-end retrieval was 7.5 ms for REST and 26.7 ms for native MCP; the layered MCP variant was about 4.1× REST. In the larger scenario, the model card including deployment information averaged 13.63 MB, and database retrieval time rose to 7843.83 ms. The paper argues that persistent sessions via Server-Sent Events (SSE) matter because dynamic model cards are expected to support active, context-preserving interactions over time [2511.21661].

A different title-case usage appears in HPC storage research, where Icicle is a scalable framework for continuous file system metadata indexing and monitoring. It is designed for environments with billions of files and hundreds of petabytes of data and combines periodic snapshot ingestion with event-based ingestion from systems such as Lustre and IBM Storage Scale (GPFS). Built on Apache Kafka and Apache Flink, it maintains a primary index for per-object discovery and an aggregate index storing summaries for users, groups, and directories. The aggregate index records distribution statistics ({\min, p25, p50, p75, \max, \text{mean}}), plus total for file size, and the implementation evaluates DDSketch, KLLSketch, ReqSketch, and t-Digest, selecting DDSketch by default because it provides the best value accuracy. On production-scale datasets—FS-small at 67.63 TB and 8.46M rows, FS-medium at 1.55 PB and 145.59M raw rows / 128.50M preprocessed rows, and FS-large at 53.59 PB and 1.04B rows—the snapshot pipeline required about 8 minutes, 29 minutes, and 217 minutes with 128 KPUs. In monitoring experiments on a single Lustre MDT, FSMonitor achieved 391–565 changelogs/s, while Icicle achieved 32–33K changelogs/s and up to 41K changelogs/s with reduction. For GPFS, a single fileset reached 55.7K changelogs/s without reduction and 62.9K changelogs/s with reduction, while five filesets reached 279.5K and 315.7K changelogs/s, respectively [2604.10295].

5. Icicle as a firmware-fuzzing emulator

In systems security, Icicle is a fuzzing-specific, multi-architecture emulation framework designed for grey-box firmware fuzzing. Its motivation is that modern emulation-based fuzzers have evolved by re-purposing general-purpose emulators such as QEMU and Unicorn, making instrumentation difficult to add cleanly and often architecture-specific. Icicle therefore treats fuzzing instrumentation as a first-class concern rather than a retrofit [2301.13346].

Its architecture combines SLEIGH processor specifications from Ghidra, P-code as the intermediate representation, Cranelift as the JIT backend, and a software MMU with byte-level mappings and a TLB. The workflow loads the ISA’s SLEIGH specification, registers Tracer Plugins, translates guest instructions to P-code, lets plugins inspect or modify translated blocks, JIT-compiles modified blocks to native code, and deliberately does not discard the P-code after compilation. Instrumentation is architecture-agnostic because plugins target P-code rather than ISA-specific opcodes. The paper describes four instrumentation styles: branch hit counts / edge coverage, context-sensitive branch coverage, CmpLog, and CompareCov. For CmpLog, the system uses a Datalog-based analysis over P-code rather than matching machine-specific compare instructions [2301.13346].

The evaluation is intended to show portability, correctness, and bug-finding value. On a synthetic benchmark compiled for x86-64, AArch64, MIPS, RISC-V, and MSP430, Icicle’s architecture-agnostic instrumentation supported comparison solving and context sensitivity across all five ISAs. On LAVA-M binaries—base64, md5sum, uniq, and who—results closely matched QEMU on x86 and AArch64 while remaining available on MIPS and RISC-V. When integrated into Fuzzware as Fuzzware-, Icicle reproduced all 16 bugs found by the original Fuzzware on the same 10 real-world ARM firmware binaries and found one additional bug in the Console binary with CompareCov enabled; it also found an additional crash in Soldering Iron, later judged a false positive due to peripheral modeling. The MSP430 campaign is especially notable because MSP430 was not supported by existing emulation-based fuzzers: Icicle discovered 7 new bugs total, including 2 in H4_PacketProtocol and 5 in Goodwatch, while reaching almost all blocks in a commercial Polar heart rate tracker firmware dump [2301.13346].

6. Natural icicles: growth, ripples, and internal inclusions

In the physical sciences, an icicle is treated as a nonequilibrium growth form controlled by latent-heat removal through a thin flowing water film. Controlled laboratory studies used a table-top refrigerated apparatus to grow 93 icicles while varying ambient temperature, water purity, flow rate, and air motion. These experiments compared observed outlines to a self-similar theory predicting an attractor profile that, in practice, reduces to the power law (r \propto z^{3/4}). Some icicles matched that theory remarkably well, but many showed substantial deviations, including non-monotonic shapes, asymmetry, and branching. Water purity mattered strongly: distilled-water icicles fit the self-similar form better, with mean reduced (\chi^2 \approx 14), whereas tap-water icicles fit worse, with mean reduced (\chi^2 \approx 50). Ripples were common on tap-water icicles—48 of 53 had clear, regular ripples—while only 2 of 23 distilled-water icicles did. A special long vertical ice finger showed ripples moving upward during growth [1008.1922].

Subsequent experiments directly challenged the idea that ripple formation is a pure thermal or surface-tension instability. In those experiments, pure water does not produce growing ripples, measurable ripple growth appeared only once ionic impurity levels reached as little as
$$
2.0\times 10^{-3}\ \text{wt \% NaCl},
$$
and the addition of the non-ionic surfactant Triton X-100, which reduced surface tension by more than 45%, still produced no measurable ripple growth. Saturation with dissolved gases also produced no growing ripples. By contrast, saline water generated clear ripples with average wavelength
$$
\bar{\lambda} = 0.985 \pm 0.004\ \text{cm},
$$
and a global mean
$$
1.04 \pm 0.01\ \text{cm}.
$$
Ripple phase speed was typically upward, depended only weakly on salinity, and the growth rate increased only very weakly, approximately logarithmically at low concentration [1301.4734].

Theoretical treatments explain the near-universal wavelength through a free-surface-coupled morphological instability. One formulation derives
$$
\lambda_{\max}=2\pi\left(\frac{a^{2}h_{0}}{3}\right)^{1/3},
$$
with (a=\sqrt{\gamma/(\rho_l g)}) the capillary length and (h_0) the mean water-film thickness. For (Q/l \sim 10 \text{ to } 100\ \text{(ml/hr)/cm}), the theory predicts (\lambda_{\max}\approx 5\text{--}13\ \text{mm}), consistent with observations near (7\text{--}10) mm and a mean about 8.5 mm. A related extension includes natural convection airflow ahead of the water-air surface and concludes that airflow strengthens heat transfer and affects phase velocity, but does not significantly change the ripple wavelength. In a representative case (Q/l=50) ((\mathrm{ml/h})/\mathrm{cm}), (\theta=\pi/2), and (\delta_0=6.6\ \mathrm{mm}), the model gives 8.6 mm with airflow versus 9.6 mm without airflow, and the most unstable mode moves upward [1103.5208] [1102.5114].

Internal-structure experiments add a further constraint on mechanism. Using 51 laboratory icicles grown from distilled water with NaCl, Dextrose, or sodium fluorescein, then sectioned and imaged, investigators showed that the foggy interior of rippled icicles is due not to air bubbles but to liquid inclusions: small pockets of highly impure liquid trapped inside the ice. The inclusions form crescent-shaped structures at low impurity and chevron-shaped bands at higher impurity; chevron apexes / crescent peaks align with ripple peaks, while pure-ice lines align with ripple valleys. Inclusion diameters were about 20 μm to 180 μm, the bulk-to-feed concentration ratio was
$$
k = 0.27 \pm 0.05,
$$
the ripple wavelength measured from edges was 9.35 ± 0.57 mm, and well-behaved cross sections gave 8.54 ± 0.66 mm. Chevron bands made an angle of
$$
58 \pm 2.8^\circ
$$
to the icicle axis, closely matching the 56 ± 2° angle inferred from directly tracked ripple peaks, reinforcing the interpretation that the interior structure records upward ripple migration [2207.05793].

Taken together, these results imply that ripple formation is not captured by a fully wetted, pure-water picture. The cited literature instead points to a coupled hydrodynamic–thermodynamic–solutal instability in a system with intermittent wetting, surface rivulets, localized impurity concentration buildup, and possibly mushy-layer physics [2207.05793] [1301.4734].

7. Derived geometric analogues and programmable-matter “icicles”

The term also appears as a deliberately chosen intermediate shape in programmable matter. In the 3D hybrid model, a single active agent with finite-state control, limited view, and the ability to carry one tile must reorganize passive rhombic-dodecahedral tiles into an icicle. Here the icicle is defined as a connected set of towers whose uppermost tiles lie in the same partially filled parallelogram, with every tile outside that top fragment having a tile directly below it. The shape is chosen because it is dense and hole-free, has low diameter compared to a line, and contains multiple removable tiles, making it easier for a weak agent to explore safely. The proposed BuildIcicle algorithm repeatedly forms a parallelogram platform and then projects it downward, converging in (\mathcal{O}(n^3)) steps from any initially connected configuration. The paper reports 12,250 simulations on random configurations of size 10 to 550 and finds that the algorithm usually reduces diameter on average [2401.17734].

Soft-matter research provides an analogue rather than a direct reuse of the term. Repeated coat → flow → cure cycles in a curable elastomer yield downward-growing, corrugated structures named flexicles for their resemblance to icicles. The instability is a stacked Rayleigh–Taylor instability, and the resulting morphologies are described as truncated cones topped by a pendant drop. Their mean spacing approaches
$$
\lambda_M = 2\pi \sqrt{2}\,\ell_c,
$$
the average surface opening angle is approximately (5^\circ), the thin-film region has thickness (\bar{h}_f \approx 0.1\ \text{mm}), and the mean height follows
$$
H = (0.8 \pm 0.02)\,N\ell_c.
$$
The Voronoi-cell shape factor
$$
\xi = \frac{p_i^2}{4\pi A_i}
$$
was reported as (1.194 \pm 0.06), indicating a quasi-ordered, irregular tiling rather than perfect hexagonal order. The work is not about natural ice, but it treats icicle-like growth as a generic consequence of coupling thin-film hydrodynamics, instability, and solidification [2403.09837].