Convenience wrappers around recursive.mask.grid.surface.*() using the
connected \(3 \times 3\) axial-cross mask: center plus the four cardinal
neighbors. This produces a mesh-derived fractal family with strong
bottlenecks while remaining orthogonally connected at every level.
Usage
vicsek.surface.embedding(
level = 2,
surface = c("saddle", "paraboloid", "ripple"),
amplitude = 0.75,
freq_u = 1,
freq_v = 1,
x_scale = 1,
y_scale = 1
)
vicsek.surface.graph(
level = 2,
surface = c("saddle", "paraboloid", "ripple"),
amplitude = 0.75,
freq_u = 1,
freq_v = 1,
x_scale = 1,
y_scale = 1,
normalize = c("median", "mean", "none")
)Arguments
- level
Recursion depth. Must be at least
1.- surface
Surface family used for the lift. One of
"saddle","paraboloid", or"ripple".- amplitude
Finite numeric amplitude controlling the non-flat displacement.
- freq_u
Positive ripple frequency in the horizontal parameter direction. Used only when
surface = "ripple".- freq_v
Positive ripple frequency in the vertical parameter direction. Used only when
surface = "ripple".- x_scale
Positive horizontal scaling of the parameter domain.
- y_scale
Positive vertical scaling of the parameter domain.
- normalize
Normalization applied to the induced edge lengths. One of
"median","mean", or"none".
Value
vicsek.surface.embedding() returns an n x 3 numeric matrix
with columns x, y, and z, where n = 5^level.
vicsek.surface.graph() returns the same components as
recursive.mask.grid.surface.graph(), with family set to
"vicsek" and a family-specific class and label.
Details
`vicsek.surface.embedding()` returns the 3D coordinates of the occupied
cells in the same vertex order as edges.vicsek().
`vicsek.surface.graph()` returns a reusable weighted-graph bundle for the
named Vicsek family.