toolbox_chaos v0.1.0
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Toolbox Chaos procedure

First Simulation and Result Record

Go from the desktop installer to a first catalog simulation, reuse the same trajectory in another view, and save a research-ready figure.

Level Beginner
GUI tab Atractor 3D for the first run; Retratos 2D or Series temporales for reuse
Research question How do I obtain a first result that I can inspect, save, and reproduce?

Question and result

Calculation performed

Complete one traceable simulation through the graphical interface and learn the controls that appear throughout the application.

Required configuration

  • Install the build for your operating system and open Toolbox Chaos from the normal application shortcut.
  • Choose a folder where you can keep figures and a short text record of the parameters used.
  • The desktop application provides this workflow directly through its graphical controls.

Panel and figure

Displayed quantities

Current Toolbox Chaos Atractor 3D tab with Lorenz controls and result
The current desktop interface keeps model and numerical controls on the left and the generated result on the right.
Title-free Lorenz trajectory in three-dimensional phase space
This phase-space view supplies the geometry; pair it with the Time Series tab because geometry and temporal evolution answer different questions.

Configuration and calculation

Control sequence

  1. Open the first simulation panel

    Select Atractor 3D. The left panel contains the system, parameter, initial-condition, method, step-size, and duration controls; the right panel is the plot area.

    On a narrow display, scroll the control panel to preserve access to every visible control.

  2. Load a catalog model

    Choose Lorenz. The catalog fills its documented parameter order, initial state, and numerical defaults automatically.

    For the first run, retain sigma = 10, rho = 28, beta = 8/3 and a small nonzero initial state. Record any value you change.

  3. Declare the numerical contract

    Select Runge–Kutta 4, use a step near 0.01, and use a duration long enough to pass the initial transient.

    The method, step, duration, initial state, and parameters jointly define the experiment and provide the record required for reproduction.

  4. Generate and inspect

    Press Generar atractor 3D and wait for the status message to confirm completion.

    Rotate the view, check that the trajectory remains finite, and look for both Lorenz lobes. A blank, exploding, or needle-like result is a reason to review the contract before continuing.

  5. Reuse the trajectory

    Open Retratos 2D or Series temporales, keep the same system selected, and press Usar última trayectoria.

    This avoids accidentally comparing different integrations while learning how geometric and temporal views complement one another.

  6. Save the result

    Use Guardar gráfica... and choose PNG for slides or web use, PDF for scalable document insertion, or another offered raster format.

    Store a companion note with the system, complete parameter vector, initial condition, method, step, duration, application version, and which transient portion you interpreted.

Record

Computed data

  • A bounded Lorenz trajectory with two lobes in 3D and matching state traces or pairwise projections when the shared trajectory is reused.
  • At least one saved image plus enough numerical metadata to repeat the run.
  • A clear distinction between selecting a named example and making a scientific classification about its behavior.

Scientific reading

Interpretation criteria

The 3D curve records the computed history of the state vector in phase space. The two lobes describe regions repeatedly visited by this finite trajectory.

Irregular lobe switching supplies a useful observation. Confirm conclusions with time series, step refinement, longer horizons, and a suitable diagnostic.

Files

Experiment record

  • Save the figure with a descriptive name such as lorenz_rho28_rk4_h001.
  • Record parameter order as displayed by the GUI when the model is later reloaded.
  • Record whether the output is a fresh local simulation or a reused shared trajectory.
  • Keep raw experiment notes with the final figure to preserve provenance through later styling.

Applications

Questions addressed by the calculation

  • First laboratory exercise on phase space and sensitivity to initial conditions.
  • Baseline run before a parameter sweep, method comparison, spectrum, or Lyapunov calculation.
  • Rapid visual screening of a catalog system before designing a reproducible research protocol.

Scope

Evidence conditions

  • The 3D tab displays three-state views; 2D portraits and time series provide the corresponding views for other displayed dimensions.
  • Evidence of attraction, asymptotic chaos, multistability, or robustness combines trajectories with declared refinements and diagnostics.
  • The separate Hidden Attractors FO engine carries the localization and certification workflow for hidden attractors.