How Do I Draw a Lorenz Attractor on an Oscilloscope and a Laser?
In BeamTracer OSC-1, switch to Performance, open GENERATORS → ATTRACTOR, and choose SYSTEM → Lorenz. Select X/Z for the familiar butterfly view, set LENGTH to 40 and FREQUENCY to 5 Hz, then choose GENERATE. OSC-1 turns that path into a repeating stereo signal. Under LASER OUTPUT, connect SIMULATOR to inspect the projected figure without hardware.
X/Z, X/Y, then Y/Z. These are three projections of the same selected system, recorded separately in OSC-1. Each uses Length 40, Frequency 5 Hz, and Size 85%.
A Lorenz attractor makes a good first chaos drawing because you can recognize its two lobes, then change the projection and see how much the view matters. You can generate the stereo drawing directly, hear its signal, and inspect its laser preview in the same app.
How do I generate the butterfly shape?
The generator starts on Lorenz with X/Z selected. You can get a complete figure without typing equations or importing a model.
- Open OSC-1 and select Performance in the header.
- In SOURCES, expand GENERATORS, then ATTRACTOR.
- Choose SYSTEM → Lorenz and PROJECTION → X/Z.
- Set LENGTH → 40, FREQUENCY → 5 Hz, and SIZE → 85%.
- Choose GENERATE. The button changes to STOP, and the scope draws the repeating trace.
- Try X/Y and Y/Z while it plays. Return to X/Z to match the opening view.
The Lorenz system describes a trajectory with three coordinates. The generator's projection chooses which two become the horizontal and vertical signal. With X/Z, the horizontal channel uses the system's X coordinate and the vertical channel uses Z. The oscilloscope itself still displays an ordinary two-channel XY drawing.
Edward Lorenz introduced the underlying system in his 1963 paper Deterministic Nonperiodic Flow. Its trajectories provide the shape; OSC-1 prepares a finite section for repeated tracing.
Does this keep growing into a new chaotic path?
OSC-1 repeats the generated section. LENGTH chooses how much trajectory goes into that section. The trace returns along its path so the loop closes without adding a straight jump from the last point to the first.
For an evolving particle presentation, open Phase Flow and try its Lorenz or Lorenz Twin preset. Phase Flow has its own camera, particle and history controls. It is a separate visualizer, not a recording of the OSC-1 stereo signal.
What does Frequency change?
FREQUENCY is how often the whole generated loop is traced each second. LENGTH changes how much trajectory goes into that loop. The examples use 5 Hz so the long, dense path has enough samples to draw smooth curves.
If you raise FREQUENCY to 20 Hz with LENGTH still at 40, the curves can become visibly angular. Each loop has fewer audio samples available at the faster rate. Lower FREQUENCY or shorten LENGTH when that happens, and watch the TRACE point count as you adjust. Display interpolation cannot restore detail already lost from the source path.
| Control | How to use it |
|---|---|
| SYSTEM | Choose Lorenz first, then compare another system using the same projection and frequency. |
| PROJECTION | Choose X/Z for the butterfly view here. X/Y and Y/Z use different coordinate pairs. |
| LENGTH | Raise it to include a longer section of the trajectory; lower it when the drawing becomes crowded. |
| FREQUENCY | Raise it to repeat the section faster. A higher rate leaves fewer audio samples for each loop. |
| SIZE | Changes how much of the XY field the drawing occupies. It does not change the equations. |
Press Play to hear the generated stereo signal at 5 Hz loop repetition. This is the drawing's audio, with no backing track. The repeating shape can look steady even while the signal keeps tracing it.
The frequency shown here describes repetition of the whole path. The bends within that path also shape the sound, so it isn't equivalent to listening to a plain 5 Hz sine wave. Keep the two channels separate if you send the signal to an external XY display: mixing them to mono loses the independent coordinates.
How do I check the laser version without a projector?
Open LASER OUTPUT in the right properties column, select SIMULATOR, and choose CONNECT SIMULATOR. The preview can show the assembled path while output remains unarmed. Select Expand preview to inspect the figure at a larger size.
Software preview with Mirrors set to Ideal. The Simulator is connected; ARM and START were not used. This does not show a physical projector.
IDEAL lets you inspect the intended path. PHYSICS adds the selected scanner model's behavior. Choose settings that correspond to your equipment when comparing a real projection; a simulated result cannot certify a projector setup. PREVIEW SPEED changes the preview's playback, while the generator's FREQUENCY controls repetition of the source signal.
For physical output, follow the laser DAC setup guide. A compatible DAC and projector, suitable scanner settings, and a controlled projection area are separate requirements from making the drawing on screen.
How do I record the drawing?
With the generator playing, open EXPORT → VIDEO, choose a frame shape and resolution, then RECORD LIVE INPUT. Choose STOP RECORDING to download the clip. This captures the live generated source and its audio; the example above uses this path. RENDER VIDEO is for a loaded track and can remain unavailable for this live generator.
For another drawing made from stereo signals, try the oscilloscope music introduction. The OSC-1 documentation covers the other sources and output options.