# quasirandom

##### Quasirandom Patterns

Generates quasirandom sequences of numbers and quasirandom spatial patterns of points in any dimension.

##### Usage

`vdCorput(n, base)`Halton(n, bases = c(2, 3), raw = FALSE, simplify = TRUE)

Hammersley(n, bases = 2, raw = FALSE, simplify = TRUE)

##### Arguments

- n
Number of points to generate.

- base
A prime number giving the base of the sequence.

- bases
Vector of prime numbers giving the bases of the sequences for each coordinate axis.

- raw
Logical value indicating whether to return the coordinates as a matrix (

`raw=TRUE`

) or as a spatial point pattern (`raw=FALSE`

, the default).- simplify
Argument passed to

`ppx`

indicating whether point patterns of dimension 2 or 3 should be returned as objects of class`"ppp"`

or`"pp3"`

respectively (`simplify=TRUE`

, the default) or as objects of class`"ppx"`

(`simplify=FALSE`

).

##### Details

The function `vdCorput`

generates the quasirandom sequence
of Van der Corput (1935) of length `n`

with the given
`base`

. These are numbers between 0 and 1 which are in
some sense uniformly distributed over the interval.

The function `Halton`

generates the Halton quasirandom sequence
of points in `d`

-dimensional space, where
`d = length(bases)`

. The values of the \(i\)-th coordinate
of the points are generated using the van der Corput sequence with
base equal to `bases[i]`

.

The function `Hammersley`

generates the Hammersley set
of points in `d+1`

-dimensional space, where
`d = length(bases)`

. The first `d`

coordinates
of the points are generated using the van der Corput sequence with
base equal to `bases[i]`

. The `d+1`

-th coordinate
is the sequence `1/n, 2/n, ..., 1`

.

If `raw=FALSE`

(the default) then the Halton and Hammersley
sets are interpreted as spatial point patterns of the
appropriate dimension. They are returned as objects of
class `"ppx"`

(multidimensional point patterns)
unless `simplify=TRUE`

and `d=2`

or `d=3`

when they are returned as objects of class `"ppp"`

or `"pp3"`

.
If `raw=TRUE`

, the coordinates are returned as a matrix
with `n`

rows and `D`

columns where `D`

is the spatial
dimension.

##### Value

For `vdCorput`

, a numeric vector.

For `Halton`

and `Hammersley`

,
an object of class `"ppp"`

, `"pp3"`

or
`"ppx"`

; or if `raw=TRUE`

, a numeric matrix.

##### References

Van der Corput, J. G. (1935) Verteilungsfunktionen.
*Proc. Ned. Akad. v. Wetensch.* **38**: 813--821.

Kuipers, L. and Niederreiter, H. (2005)
*Uniform distribution of sequences*,
Dover Publications.

##### See Also

##### Examples

```
# NOT RUN {
vdCorput(10, 2)
plot(Halton(256, c(2,3)))
plot(Hammersley(256, 3))
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*