# Guess regions associated with attractors.

### Description

Attempts to guess which areas of the range are drawn to which attractors. The attractors
must be added to the model before `guessregions()`

is added. The space is discretized
into squares, and
repeated iteration of the model's function is used to determine which attractor the middle
of each square tends towards. The square is then given the color of that attractor. The model
is assumed to be well behaved in that every point will eventually move within `epsilon`

of an attractor. **There is absolutely no guarantee that all regions will be captured
by this approach**, even with a fine-grained discretization. It is possible to blur
boundaries, crop regions, or miss entire regions.

### Usage

1 2 3 |

### Arguments

`discretize` |
The size of each square. If not set, the discretization of the range is used. May be set separately from the discretization of the range without overwriting. |

`xlim` |
The range of x values to calculate regions over. Defaults to the limits of the range. |

`ylim` |
The range of y values to calculate regions over. Defaults to the limits of the range. |

`iters` |
If not set, each point will be iterated indvidually. If set as a number, exactly
that many iterations will be used. If set as |

`epsilon` |
When |

`behind` |
Forces this item to be a background object for the purposes of layering |

`stable` |
A, usually smaller, distance at which a point is considered to have stopped moving. Defaults to |

`cols` |
The colors to use for the various regions. The colors will be used in the order the attractors were added to the model. |

`missingCol` |
When |

`...` |
Extra graphical parameters for |

### Details

All attractors should be `dspoints`

with the `attractor`

flag set to `TRUE`

,
and should already be composed with the model. Attractors may
have `display=FALSE`

set to avoid displaying the attractor itself. Their color (or region
color, if defined) will be
used as the color of the region. If there are no points with the `attractor`

flag set,
then all points are used as possible attractors. This is not recommended.

If `iters`

is not set, or is set to `NULL`

, then each point will be individually
iterated until within `epsilon`

distance of an attractor, or until it moves less
than `stable`

between iterations. Points that stop moving further
than `epsilon`

of an attractor, are colored `missingCol`

, default
"lightgoldenrod3".

If `iters`

is given a numeric value, each point is iterated exactly `iters`

time,
and the closest attractor is chosen regardless of distance. In this case, `epsilon`

has
no effect. This will take bounded time, but may give a poorer guess.

If `iters`

is given an infinite value, the points are iterated until they move less than
`stable`

distance. An attractor is chosen only if it falls within `epsilon`

distance,
otherwise the point is colored `missingCol`

.

The `image`

function is used to display the results.

### See Also

`dspoint`

`dsregion`

`dspolygon`

`guessattractors`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
library(dsmodels)
model <- dsmodel(function(X0,Y0) {
list(X0*exp(2.6-X0-6.45/(1+4.5*X0)),
Y0*exp(2.6-Y0-0.15*X0-6.25/(1+4.5*Y0)))
})
model+dsrange(0:3,0:3,discretize = .08)+
dspoint(1.9358, 1.5059, attractor=TRUE, col="green", label = "K12")+
dspoint(1.9358, 0, attractor=TRUE, col="magenta",label = "K1")+
dspoint(0, 1.9649, attractor=TRUE, col="orange", label = "K2")+
dspoint(0, 0, attractor=TRUE, col="blue", display=FALSE)+
dspoint(0.4419, 0.4416, col="yellow", label="A11")+
guessregions(discretize=0.02)
``` |