R: Fry Plot of Point Pattern

fryplot {spatstat.core} | R Documentation

## Fry Plot of Point Pattern

### Description

Displays the Fry plot (Patterson plot) of a spatial point pattern.

### Usage

    fryplot(X, ..., width=NULL, from=NULL, to=NULL, axes=FALSE)
    frypoints(X, from=NULL, to=NULL, dmax=Inf)

### Arguments

`X` | A point pattern (object of class `"ppp"`) or something acceptable to `as.ppp`.
`...` | Optional arguments to control the appearance of the plot.
`width` | Optional parameter indicating the width of a box for a zoomed-in view of the Fry plot near the origin.
`from,to` | Optional. Subset indices specifying which points of `X` will be considered when forming the vectors (drawn from each point of `from`, to each point of `to`.)
`axes` | Logical value indicating whether to draw axes, crossing at the origin.
`dmax` | Maximum distance between points. Pairs at greater distances do not contribute to the result. The default means there is no maximum distance.

### Details

The function `fryplot` generates a Fry plot (or Patterson plot); `frypoints` returns the points of the Fry plot as a point pattern dataset.

Fry (1979) and Hanna and Fry (1979) introduced a manual graphical method for investigating features of a spatial point pattern of mineral deposits. A transparent sheet, marked with an origin or centre point, is placed over the point pattern. The transparent sheet is shifted so that the origin lies over one of the data points, and the positions of all the other data points are copied onto the transparent sheet. This procedure is repeated for each data point in turn. The resulting plot (the Fry plot) is a pattern of n(n-1) points, where n is the original number of data points. This procedure was previously proposed by Patterson (1934, 1935) for studying inter-atomic distances in crystals, and is also known as a Patterson plot.

The function `fryplot` generates the Fry/Patterson plot. Standard graphical parameters such as `main`, `pch`, `lwd`, `col`, `bg`, `cex` can be used to control the appearance of the plot. To zoom in (to view only a subset of the Fry plot at higher magnification), use the argument `width` to specify the width of a rectangular field of view centred at the origin, or the standard graphical arguments `xlim` and `ylim` to specify another rectangular field of view. (The actual field of view may be slightly larger, depending on the graphics device.)

The function `frypoints` returns the points of the Fry plot as a point pattern object. There may be a large number of points in this pattern, so this function should be used only if further analysis of the Fry plot is required.

Fry plots are particularly useful for recognising anisotropy in regular point patterns. A void around the origin in the Fry plot suggests regularity (inhibition between points) and the shape of the void gives a clue to anisotropy in the pattern. Fry plots are also useful for detecting periodicity or rounding of the spatial coordinates.

In mathematical terms, the Fry plot of a point pattern `X` is simply a plot of the vectors `X[i] - X[j]` connecting all pairs of distinct points in `X`.

The Fry plot is related to the K function (see `Kest`) and the reduced second moment measure (see `Kmeasure`). For example, the number of points in the Fry plot lying within a circle of given radius is an unnormalised and uncorrected version of the K function. The Fry plot has a similar appearance to the plot of the reduced second moment measure `Kmeasure` when the smoothing parameter `sigma` is very small.

The Fry plot does not adjust for the effect of the size and shape of the sampling window. The density of points in the Fry plot tapers off near the edges of the plot. This is an edge effect, a consequence of the bounded sampling window. In geological applications this is usually not important, because interest is focused on the behaviour near the origin where edge effects can be ignored. To correct for the edge effect, use `Kmeasure` or `Kest` or its relatives.

### Value

`fryplot` returns `NULL`. `frypoints` returns a point pattern (object of class `"ppp"`).

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### References

Fry, N. (1979) Random point distributions and strain measurement in rocks. Tectonophysics 60, 89–105.

Hanna, S.S. and Fry, N. (1979) A comparison of methods of strain determination in rocks from southwest Dyfed (Pembrokeshire) and adjacent areas. Journal of Structural Geology 1, 155–162.

Patterson, A.L. (1934) A Fourier series method for the determination of the component of inter-atomic distances in crystals. Physics Reviews 46, 372–376.

Patterson, A.L. (1935) A direct method for the determination of the components of inter-atomic distances in crystals. Zeitschrift fuer Krystallographie 90, 517–554.

### See Also

`Kmeasure`, `Kest`

### Examples

    ## unmarked data
    fryplot(cells)
    Y <- frypoints(cells)

    ## numerical marks
    fryplot(longleaf, width=4, axes=TRUE)

    ## multitype points
    fryplot(amacrine, width=0.2,
                      from=(marks(amacrine) == "on"),
                      chars=c(3,16), cols=2:3,
                      main="Fry plot centred at an On-cell")
    points(0,0)

[Package spatstat.core version 2.3-0 Index]