Sprott Explorer

Understand how compact Sprott-style codes are decoded into maps or flows, simulated, filtered, searched, and rendered as candidate chaotic dynamics.

Purpose Generate and inspect candidate dynamics

Evidence Level Visual triage, not proof

Objective

Decode, simulate, filter, visualize, and organize Sprott-style maps or flows as reproducible candidates for later numerical investigation.

Workspace

GUI tab

Explorador Sprott

Procedure

Open a built-in example, generate a compact code, or load a user-owned local dictionary record.
Decode the family, dimension, order, coefficients, equations, and whether the definition is a map or a flow.
Use the fixed starting vector with every component equal to 0.1, then choose iterations or total time, transient, and an appropriate step and method for flows.
Simulate, reject divergence or collapse, and inspect more than one projection, point-density setting, and color mode.
Store promising simulations in the local gallery and export the numerical and explanatory artifacts needed to reproduce the view. Use Local Inventory only to index reference files and send a selected .DIC to Examples.

Result

Expected result

An explicit decoded map or flow together with a finite simulated trajectory and one or more candidate visualizations.
A local record that preserves the code, numerical settings, projection, and visual configuration used for the candidate.

Interpretation

A bounded structured rendering is a candidate for deeper analysis. It becomes more credible when the structure survives transient, step, duration, projection, and re-simulation checks; the current GUI does not test alternative initial conditions.

The code, decoded equations, and simulation settings are the scientific object; point size, alpha, and color improve readability but do not change the underlying trajectory.

Export

Export and reproducibility

Export figures as PNG, PDF, or SVG; preserve metadata as JSON, trajectory values as CSV, and the generated explanation as Markdown when those artifacts are needed.
Record the code, family, decoded equations, dimension, map/flow type, fixed starting vector (0.1 in every component), method, step or iterations, duration, transient, divergence threshold, random seed, stopping criterion, maximum attempts, projection, and visual preset.

Applications

Teaching how compact codes become explicit maps, flows, trajectories, and projections.
Screening many generated definitions before allocating longer numerical studies.
Building a reproducible local gallery or dataset of candidate dynamics and their settings.

Limits

Visual triage can retain numerical artifacts, long transients, periodic orbits, or projection effects that resemble chaotic structure.
Passing the local filters does not prove chaos, attraction, robustness, or uniqueness.
Sprott Explorer does not localize, classify, or certify hidden attractors.

Current Toolbox Chaos Sprott Explorer interface — The current Sprott Explorer organizes nine workspaces: Home, Tutorial, Theory, Codes, Exploration, Examples, Gallery, Local Inventory, and Backend Explained.

Synthetic Sprott visual preset rendered by the toolbox — Synthetic public example rendered with the Sprott visual preset system. The public site uses generated educational examples and does not redistribute original dictionary files.

Generated Sprott-style 3D map with color-coded coordinate — 3D map projection: color keeps a coordinate readable when the geometry is dense.

Generated Sprott-style 4D map projected with fourth-coordinate color — 4D projection: the visible plane shows two coordinates while a fourth coordinate is encoded with color.

Fastest Path Through the Interface

Open Sprott Explorer and choose Home → 1. Try an example, or open Examples and select a recommended synthetic case.
Select Simulate with recommended style to load a coherent projection, palette, density, transient, and numerical scale.
Change one display or simulation control at a time and compare whether the geometric structure remains readable.
Export an image and, when the run will be analyzed elsewhere, the trajectory CSV and metadata JSON.
Save useful cases in the local gallery so they can be re-simulated and compared without altering source dictionaries.

Tools Available in Sprott Explorer

Codes: decode, generate, and search compact records for maps and flows.
Exploration: select projections, palettes, color variables, density, bands, point size, and transparency.
Examples: run bundled synthetic maps and flows, including didactic fixed-point and divergence cases.
Local dictionary: read a local .DIC resource without copying or redistributing the original file.
Gallery: preserve generated cases with their simulation and visual metadata, then reopen or re-simulate them.
Local inventory: index local reference files without modifying them and send a selected .DIC to Examples.
Export: save PNG, PDF, or SVG graphics, CSV trajectories, JSON metadata, galleries, and a Markdown explanation of the pipeline.

Visual and Copy Controls

Control	What it changes	What it does not change
Fondo	Background color of the canvas and exported figure.	The decoded equations and simulated trajectory.
Modo dibujo	Representation as points, line, line plus points, or density view.	The numerical samples already produced by the simulation.
Máx puntos	Visual subsampling after the transient so a dense render remains responsive and readable.	The stored or exported simulated data; it limits drawing only.
Bandas	Quantization of a continuous color scale into a declared number of bands; zero keeps continuous color.	Coordinates, iteration order, and dynamics.
DPI export	Raster resolution used for PNG and PDF-oriented exports.	Simulation accuracy or number of trajectory samples.
Mostrar ejes, Mostrar grid, Aspect ratio igual	Axes, reference grid, and geometric scaling of the view.	The underlying trajectory; equal aspect changes how distances are drawn, not their values.
Copiar código, Copiar cita	The compact code or supplied citation placed on the clipboard for a record or caption.	The current equations, numerical settings, and rendered result.

What a Sprott Code Means

A Sprott-style code is a compact recipe for a dynamical system. It is not an image and it is not a label of chaos. The code is decoded into algebraic terms, coefficients, dimension, and update type. Only after that conversion does the toolbox simulate the resulting map or flow.

The educational value is that a short symbolic record can generate many different phase portraits. Students can see how simple deterministic functions produce fixed points, cycles, dense clouds, folded bands, or apparently chaotic attractors.

1. Family

The first symbol selects a family. In the toolbox grammar, families A-D are 1D maps, E-H are 2D maps, I-L are 3D maps, M-P are 4D maps, Q-T are 3D flows, and U-X are 4D flows.

2. Dimension and order

The family implies the number of variables and the polynomial terms that may appear. Maps are iterated directly; flows are integrated as differential equations.

3. Coefficients

The remaining characters encode coefficients. The decoder maps characters into numeric weights and attaches those weights to the monomials allowed by the selected family.

4. Function

The decoded record becomes an explicit function: x(n+1)=F(x(n)) for maps, or dx/dt=f(x) for flows. This function is what the toolbox actually simulates.

Search Logic

The searcher is a triage workflow. It does not prove chaos. It tries many compact recipes, simulates them with bounded numerical settings, rejects obvious failures, and keeps visually structured candidates for deeper analysis.

Generate or load a compact code.
Decode the code into equations, dimension, order, coefficients, and update type.
Simulate the map or flow from the current fixed starting vector, with every component equal to 0.1.
Discard transient points so startup motion does not dominate the figure.
Reject obvious failures such as divergence, collapse, NaN values, or empty ranges.
Render several projections and color modes to see whether the structure survives visual changes.
Promote promising candidates to longer simulations and independent diagnostics.

Presets, Criteria, and Re-simulable Attempts

A simulation preset changes a coherent group of controls at once: map or flow type, dimension, polynomial order, iterations, discarded transient, integration step, and flow method. Start with a recommended map or short RK4 flow preset, read the applied values shown below the selector, and then change one control at a time. Visual presets are separate: options such as Color por profundidad, Alta densidad, and Didáctico change projection and rendering without changing the decoded equations.

Set Semilla aleatoria before Generar código or Buscar candidato. Reusing the seed with the same family, dimension, order, and search controls reproduces the generated code sequence; when local .DIC entries participate, also record the filter and selected starting row.
Set Intentos máximos to bound how many codes Buscar candidato may test in one run. A larger value explores more candidates but also increases computation time.
Choose the minimum stopping criterion: candidate_chaotic for the quick candidate filter, acotado for a bounded result, or cualquier no divergente for the broadest non-divergent acceptance rule.
Read the attempts table instead of keeping only the final image. Each row reports attempt number, code, state, reason, x/y ranges, and a quick Lyapunov indicator.
Double-click any row to load that code back into Exploration and simulate it again under the currently declared numerical and visual settings.

The stopping criterion controls triage, not scientific certification. In particular, candidate_chaotic and the quick Lyapunov column identify records worth checking with longer simulations and independent diagnostics; they are not substitutes for a convergence-aware Lyapunov analysis.

Local .DIC Workflow

The Examples workspace reads user-provided .DIC files from disk. Select an automatically detected SELECTED.DIC, BOOKFIGS.DIC, or SPECIAL.DIC, or choose a file manually. The application reads the source in place; it does not copy the dictionary into the project or redistribute its contents.

Choose a load limit of 350, 500, 1000, or Todos. Use a smaller limit for a quick inspection and the complete option only when the full table is needed.
Filter the loaded table by simulation support, map or flow type, dimension, family, parser outcome, or the displayed F and L criteria. The status line reports how many recognized entries remain visible.
Select a row to inspect its source line, code, family, dimension, order, metrics, support state, and decoded details. Double-click it, use Simular código local seleccionado, or apply Simular con estilo recomendado.
For a local batch, choose N = 10, 25, or 50 and press Generar galería local desde este .DIC. Only the first N currently visible records are simulated, so apply the intended filter before starting.

Gallery and Local Inventory

Guardar en galería stores a locally generated render, thumbnail, decoded code, simulation configuration, visual style, and source identity. In Galería, select an entry to inspect those values, open the render, re-simulate the code, restore its style for editing, or export the displayed PNG. Re-simulation restores the saved iterations, transient, step, method, divergence threshold, and visual configuration before running the code again.

Inventario local serves a different purpose. Select a folder to list recognized local references by name, path, type, size, and category; optionally calculate a SHA-256 hash when file identity matters. The inventory does not execute or modify those files. A selected .DIC can be sent to Examples for the read-only loading and simulation workflow described above.

Book Reading Mode

After loading a local BOOKFIGS.DIC or another compatible dictionary, enable Modo lectura del libro. The view reuses the entries already in memory and lets you restrict the table to a line interval that corresponds to the part of the physical reference you are consulting.

Select a row to inspect the code, family, dimension, order, F/L values, support information, and decoded detail. Double-click to simulate it, use the recommended-style button for a family-appropriate rendering, send it to Codes for detailed decoding, save a generated image to the local gallery, or copy the supplied academic citation. The original .DIC remains unchanged.

Backend Explained and Markdown Export

Backend explicado converts the code currently shown in Exploration into a didactic account of the complete GUI pipeline: input cleaning, family decoding, monomial count, coefficient matrix, explicit equations, the fixed starting vector, simulation method, classification criteria, and visual configuration. It can explain the text of a code before a run; after a simulation, it also incorporates the active rendering settings.

Place the target code in the Exploration code field and verify iterations, transient, step, method, and current visual preset.
Press Explicar código actual and compare the displayed equations and simulation contract with the generated figure.
Press Exportar explicación Markdown to save the same structured explanation as a portable .md file for a laboratory record or teaching handout.

The explanation documents what the interface does with the code; it does not upgrade a quick classification into proof of chaos or hiddenness.

From Function to Graphic

Decode: split the compact code into family, dimension, polynomial order, and coefficient list.
Build the function: combine coefficients with allowed monomials to form F(x) for maps or f(x) for flows.
Simulate: iterate maps directly or integrate flows with Euler/RK4 using a chosen step size.
Discard transient: remove the initial segment so the figure reflects long-term behavior rather than startup motion.
Project: choose x-y, x-z, y-z, 3D, or a 4D projection where the hidden coordinate appears as color.
Filter: reject trajectories that diverge, collapse to a point, leave the plotting range, or show obvious numerical failure.

How Parameters Change This Figure

Iterations or total time

Too few points can miss the attractor. Too many points can overplot into a solid mass unless point size and alpha are reduced.

Transient length

A startup spiral or jump can look interesting but disappear after enough transient points are removed.

Step size for flows

Euler or RK4 step size changes numerical stability. A large step can create false bounded shapes or divergence.

Fixed starting vector

The current Explorer simulation fixes every starting component at 0.1 and does not expose an initial-condition control. Interpret each candidate under that declared start.

Projection

2D, 3D, and 4D color projections reveal different aspects of the same data. A fourth coordinate can be encoded by color.

Alpha and point size

Dense maps need smaller points and lower alpha so returns remain visible instead of forming an opaque block.

How to Interpret a Candidate

A candidate image is a hypothesis. If it is bounded, non-collapsed, and visually structured, it deserves further inspection. The next steps available in the GUI are to run longer simulations, reduce the integration step for flows, compare projections, estimate Lyapunov exponents in the appropriate dedicated workflow, and check whether the apparent structure survives. The Explorer itself keeps every starting component fixed at 0.1.

This is why the toolbox labels quick results conservatively. A visual candidate can guide exploration, but chaos claims require numerical diagnostics and reproducibility.

Common Errors

Calling every dense cloud chaotic: numerical noise, bad projection, or too many overplotted points can mimic complexity.
Skipping transients: a startup spiral can look interesting but disappear after enough iterations.
Claiming initial-condition robustness: Sprott Explorer uses the fixed vector with every component equal to 0.1 and exposes no start control, so its output cannot establish behavior for alternative initial conditions.
Overreading candidate_chaotic: this is a quick filter outcome, not a formal mathematical classification.

Scope Boundary: Toolbox Chaos and Hidden Attractors FO

Sprott Explorer is a GUI for generating, simulating, filtering, visualizing, and organizing candidate dynamics. It does not localize or classify hidden attractors. That scientific task belongs exclusively to the Hidden Attractors FO engine and requires a separate, documented validation workflow.