Toolbox Chaos practical guide
3D Attractor View
Generate a three-state trajectory, adjust its visual presentation, add coordinate-plane projections, and evaluate whether the geometry is numerically credible.
Objective
What you will accomplish
Use the 3D view as a controlled geometric experiment rather than as decorative evidence.
Before you begin
- Select a catalog model whose displayed dimension is exactly three.
- Choose a justified parameter set, initial state, method, step size, and duration.
Reference outputs
What these views can show
Procedure
Step-by-step workflow
-
Select a compatible system
Choose a three-state entry such as Lorenz, Rössler, Chua, or Chen. The tab disables generation when the displayed dimension is not three.
Run the registered defaults once before changing the model parameters.
-
Set the simulation inputs
Enter the parameter vector and initial state in the labels shown by the interface. Select Euler, Heun, or RK4 and declare step and duration.
Use a smaller step for strongly curved or stiff-looking segments and a longer duration when the initial transient dominates the visible curve.
-
Choose the visual options
Set the attractor color independently of the equations. Enable Superponer proyecciones when coordinate-plane shadows will help connect the 3D curve to 2D portraits.
Do not compare two runs using inconsistent camera angles or axis scales without saying so.
-
Generate and rotate
Press Generar atractor 3D, then rotate the canvas to check overlap, thin structures, symmetry, and regions hidden by the first viewpoint.
Inspect whether the trace contains an early approach segment that should be identified as transient rather than part of the recurrent geometry.
-
Test numerical stability
Repeat with half the step and compare the large-scale occupied region, not pointwise coincidence at late chaotic times.
Repeat with a longer horizon and a nearby initial condition. Report whether the qualitative geometry persists and where it differs.
-
Save the figure
Use Guardar gráfica to export at the GUI's publication-oriented resolution. Save a second view if one camera angle hides important structure.
Include variable names, parameter values, integration contract, and any transient handling in the figure caption or companion record.
Result
Expected output
- A finite three-dimensional state trajectory whose axes, parameters, initial state, and numerical resolution are known.
- Optional coordinate-plane projections that agree with separately generated pairwise portraits.
Interpretation
How to read it
Dense recurrent-looking geometry suggests that the simulated orbit revisits a bounded region. Self-crossings in a 2D projection need not be intersections of the 3D trajectory.
Late trajectories from nearby starts may separate even when they occupy a similar region; this is why geometric agreement and pointwise agreement are different tests.
Export
Reproducibility checklist
- Save at least one view with readable axes and a reproducible camera orientation description.
- Record whether coordinate-plane projections were overlaid.
- Pair the 3D image with time series or 2D portraits from the same run.
Applications
Where this workflow helps
- Communicating phase-space geometry in teaching and publications.
- Screening parameter regions before a systematic bifurcation or Lyapunov study.
- Comparing large-scale occupied regions under controlled parameter or initial-condition changes.
Limits
What it does not establish
- The renderer may decimate a very long trajectory for responsive display; preserve the numerical contract rather than inferring sample count from visible pixels.
- A bounded-looking curve is not proof of an invariant attracting set.
- This tab does not determine whether an attractor is hidden or locate hidden-attractor basins.