Stimulus Operators

All stimulus operators take a destination field and an options table; most support scale_by_dt (bool) to scale writes by the simulation timestep.

Wave Drivers Sinusoids, chirps, harmonic stacks, and waveform generators.

Spatial Patterns Checkerboards, moire fields, positional encodings, and structured masks.

Beam & Wavelet Families Localized pulses, beams, vortices, wavelets, and moving packets.

Modal Sources Chladni figures, fixed-boundary modes, and Laplace-Beltrami eigenmodes.

Shared Coordinate Mapping 🧭

Most spatial stimuli support alternate coordinate mappings. The wave, beam, modal, and pattern operators on this page all draw from the same expanded coordinate contract.

Parameter	Type	Default	Description
`coord_mode`	enum	`"axis"`	Coordinate mode: `axis`, `angle`, `radial`, `polar`, `azimuth`, `elliptic`, `separable`, `spiral`
`coord_axis`	enum	`"x"`	Axis for `coord_mode = "axis"`
`coord_combine`	enum	`"multiply"`	Separable combine rule: `multiply`, `add`
`coord_angle`	double	`0.0`	Angle for `coord_mode = "angle"` or ellipse orientation (radians)
`origin_x`, `origin_y`	double	`0.0`	Coordinate origin for 2D mappings
`spacing_x`, `spacing_y`	double	`1.0`	Coordinate spacing for 2D mappings
`coord_center_x`, `coord_center_y`	double	`0.0`	Center used by radial, polar, azimuth, elliptic, and spiral mappings
`coord_velocity_x`, `coord_velocity_y`	double	`0.0`	Center velocity for moving radial/polar/elliptic mappings
`coord_ellipse_u`, `coord_ellipse_v`	double	`1.0`	Elliptic semi-axes for `coord_mode = "elliptic"`

Spiral coordinate parameters (for operators with coord_mode = "spiral"):

Parameter	Type	Default	Description
`coord_spiral_arms`	double	`1.0`	Spiral arm multiplier applied to theta
`coord_spiral_pitch`	double	`1.0`	Spiral radial pitch multiplier
`coord_spiral_phase`	double	`0.0`	Spiral phase offset (radians)
`coord_spiral_angular_velocity`	double	`0.0`	Spiral angular drift rate (rad/s)

Wavevector overrides (for stimulus_sine, stimulus_chirp, stimulus_spectral_lines, stimulus_gabor):

Parameter	Type	Default	Description
`kx`, `ky`	double	`0.0`	Wavevector components (rad/unit)
`use_wavevector`	boolean	`false`	Use `kx`/`ky` instead of `wavenumber` + coordinate mapping

Shared Timing & Phase Controls ⏱️

Parameter	Type	Default	Description
`amplitude`	double	Peak output amplitude (before dt scaling)
`wavenumber`	double	Spatial wavenumber k (rad/unit)
`omega`	double	Angular frequency (rad/s)
`phase`	double	`0.0`	Phase offset (radians)
`time_offset`	double	`0.0`	Shift time by constant before evaluation
`nominal_dt`	double	`0.0`	Fixed timestep for `fixed_clock = true`
`fixed_clock`	boolean	`false`	Lock evolution to `nominal_dt`
`scale_by_dt`	boolean	`true`	Multiply write by dt
`rotation`	double	`0.0`	Complex phase rotation on output (radians)

Wave Drivers

Sine: Traveling or standing sinusoidal plane wave.
Standing Wave: Two counter-propagating sine waves forming a standing pattern.
Chirp: Frequency-swept sinusoid with time-varying wavenumber or frequency.
Spectral Lines: Superposition of sinusoidal harmonics with configurable decay.
Fourier Waveform: Bandlimited saw, square, and triangle synthesis.
Digamma Square Wave: Deformable digamma waveform with optional field-driven warp mixing.
Former Digamma Square Warp links now resolve to Digamma Square Wave; use warp_field, warp_mix, warp_bias, and warp_mode.
Lissajous: Gaussian ridge built around coupled oscillator traces.

Spatial Patterns

Checkerboard: Checker and stripe fields with configurable periods and phase.
Moire: Beat patterns from nearby gratings or crossed wavevectors.
Positional Encoding: Multi-scale sinusoidal coordinate encoding.
Log Spectral Grid: Logarithmically spaced polar frequency-grid synthesis.
RD Seed: One-shot reaction-diffusion seed templates.
Log-Polar (experimental): Rings-and-spokes structure from log-radius and angle.

Beam & Wavelet Families

Gaussian Pulse: Pure Gaussian envelope for localized pulses and masks.
Gabor Kernel: Gaussian-windowed sinusoid for localized frequency structure.
Morlet Wavelet Field: Multi-scale Morlet packet field with drifting orientation.
Steerable Wavelet: Direction-selective multi-scale Simoncelli or Riesz synthesis.
Heat Kernel: Diffusing Gaussian source with optional mass preservation.
Optical Vortex: Phase-singular beam with topological charge.
Airy Beam: Finite-energy Airy beam with apodized lobes.
Zone Plate: Fresnel-style quadratic radial phase plate.
Bessel Beam: Cylindrical Bessel beam with configurable order.
Hermite-Gaussian Beam: Separable transverse beam modes inside a Gaussian envelope.
Traveling Wave Packet: Gaussian-envelope packet with drifting carrier.
Cylindrical Wave Emitter: Regularized cylindrical wave radiating from a moving source.

Chladni: Nodal-line plate patterns from rectangular modes.
Laplace-Beltrami: Analytic eigenmodes on rectangles, cylinders, and flat tori.
Wave Modes: Fixed-boundary standing modes of the wave equation.