NOTE: Terms in italics are defined in Timelines Version 5.
*Groups* can interact with each other to form a new group in one of at least three ways: weighted, summed, or mixed. For two such groups with values *V* and *Weight* for a given *variable*, the results of these interctions are calculated as follows (where MAX is the maximum of two numbers).
Weighted: |
Vweight = ( Weight_{1} * V_{1} + Weight_{2} * V_{2} ) / ( Weight_{1} + Weight_{2} ) |
Summed: |
Vsum = V_{1} + V_{2} |
Mixed: |
Vmix = ( Weight_{1} * V_{1} + Weight_{2} * V_{2} ) / MAX( Weight_{1} , Weight_{2} ) |
In the Timelines model, the* state* of a *group* can be derived from combinations of three basic variables: *Population*, *Consumption*, and *Capacity*. Values of other *global variables* can be derived from combinations of these.
Changes in state of the *world group* over an interval of time is easily modeled as the interaction of the group (Group 1) at the beginning with another group (Group 2) to form a mixed group that becomes Group 1 for the next interval of time. The weights for Group 1 are all equal to 1, and the weights for Group 2 are all equal to per-capita consumption *C* for Group 2.
Values for *Population* are shown in the following graph for groups in the *Green simulation*. The circles illustrate the groups for the interaction from 1971 to 1972 (*Group 1* is plotted for year 1971, *Group 2* is plotted for 1971.5, and both *Summed *and *Mixed* group populations are plotted for 1972). The blue line shows the annual values of Group 1 populations, and the yellow line shows the values of Group 2 populations between each pair of years. Roll over the image for more years. |