# Fractional Brownian field simulation by the midpoint displacement method

### Description

The function `midpoint`

yields simulation of sample path of a fractional Brownian field
by the midpoint displacement method.

### Usage

1 |

### Arguments

`process` |
an object of class process (namely an FBm). |

### Details

The subspace [0,1] x [0,1] is discretized in a regular space discretization of size
*(2^{\code{nblevel}}+1)^2*. At each point of the grid, the fractional Brownian
field is simulated using the midpoint displacement method described for example
in Fournier et al. (1982).

### Value

an object of class process with the simulated sample path in the corresponding slot `values`

.

### Author(s)

Alexandre Brouste (http://perso.univ-lemans.fr/~abrouste/) and Sophie Lambert-Lacroix (http://membres-timc.imag.fr/Sophie.Lambert/).

### References

A. Fournier, D. Fussel and L. Carpenter (1982) Computer rendering of stochastic model, Communication of the AMC, 25, 371-384.

H.O. Peitgen and D. Saupe (1998) The science of fractal images, Springer-Verlag.

R.F. Voss (1985) Random fractal forgeries. NATO ASI Series, F17, 805-835.

### See Also

`fieldsim`

.

### Examples

1 2 3 4 5 6 | ```
# load FieldSim library
library(FieldSim)
plane.fBm<-setProcess("fBm-plane",0.9)
midpoint(plane.fBm)
plot(plane.fBm)
``` |