A part of the variables used in the simulation are dynamic, which means that they need to be calculated before each iteration of the program.

These variables are represented by maps showing the distance from a cell in a particular state to the nearest cell in a different state, and the sojourn time. In consequence, there will be one map of distances and one of sojourn time for each landscape element.

The first procedure consists of computing, in a first step, the frontier cells for each landscape element patch, whose locations are stored in a 2D tree. In a second step, the landscape map is again scanned to calculate the Euclidean distance between the null cells (a different state cell for each landscape distance map) to the nearest frontier cell stored in the 2D tree. The sojourn time maps are calculated by adding one time unit for the non-changed cells after each iteration.

The sojourn time can be used in two ways, First, it can be applied to restrict a change only after a cell has remained in a given state for a specified period of time. Second, it can also be used to derive the secondary forests from the regeneration areas, which have reached a certain age.

The method chosen uses logistic regression to obtain the maps of the areas most favorable for each type of transition. Therefore, the result of this procedure consists of a set of maps, each one depicting the probability of a location to change to another state. According to the current cell state, one of the spatial transition probability map stored in output cube data will be picked up to be used by the transitional functions (expander and patcher).

The transition rates are passed on to the program as a fixed parameter within a given phase. Because their values represent percentage of transition, It is necessary to calculate the amount of cells to be changed by each specified transition during an iteration. This is done by multiplying the number of cells of each landscape element occurring in a time step by the transition rate. To be used for projection purposes, the software also incorporates a parameter, called Saturation Value, which forces the stopping of the transition i-j, when the number of cells in state i reaches a minimum value. This effect takes into account the shape of the diffusion curve (Fig. ), and it is calculated by using the equation below.

Rate’ (forest-deforested) = Rate(forest-deforested)*(M-v)/(M+v)

Where M is the forest percentage area remaining at a time, and v is the minimum value in that the forest will remain.

Fig2. The flowchart of the DINAMICA software