Examples of scenarios - Grid
Examples of scenarios - Grid
What follows are some examples to illustrate the effects of certain probability settings within complex, dynamic systems at various sizes. The settings files can be found in the program's install folder.
Note that CauseF represents a visualisation of those effects. It functions on the principle of emerging states under the aggregate influence of environmental factors defined in terms of probabilities. See the Footnote for what this means in comparison with software designed to project outcomes using probability calculations.
All screen shots are 75% of their actual size.
Default settings, using various options
Default settings, using various options
A simple scenario to illustrate how quickly a population of 960 target elements is activated by one source. Also serves as an introduction to the settings in general.
To check how soon any one element reaches activation level 1, in the Settings window enter 1 in Activation level to track on grid, make sure Max level below is clicked, and tick Cycles → Cycle limit at activ. level to the right. In the Grid window click Reset and then Start. The cycling stops when Max number of elem's at activation level 1 has reached 1, and Cycle shows the number of cycles up to that point. It may take just 1 cycle to have at least one element reach activation level 1 (it may not be visible on the Grid because its activation level has been reduced to 0 again during this one cycle), or it may take longer.
To observe how many elements are at any given activation level during the cycles, click radio button Current level next to Max level and set the desired activation level at Activation level to track on grid. In the Grid window the text referring to the activation levels has changed to Current number of elem's at activation level * where '*' is the level selected. The number of elements will rise and fall as the system cycles, but under the current settings will gradually rise overall until the elements of the selected activation level have been replaced by elements with a higher activation level; eventually they all end up at level 9.
Depending on the sequence of selections it may be necessary to click Stop first, then Reset and then Start.
Note that once the system has stopped when an activation level has been reached and then another activation level is selected, when starting again the states of the grid up to that point will be shown but the cycle numbers will indicate how many subsequent cycles were needed to reach the newly selected activation level. However, if the latter is lower than the previous ones, the system will advance by only one cycle.
To change the number of sources use Number of source elements. In Density the spacing between the sources can be changed, from being placed right next to each other (0) to the maximum distance possible to accommodate the number of sources (if a value larger than the maximum is entered the number will automatically reset to the current maximum). Clicking Manual allows the user to set individual sources at the location on the Grid defined by Element ID (eg, a value of 480 means the source will be the 480th unit on the Grid).
Note that the location of the sources does not affect the activation levels of the targets. The latter are a result of a random selection process under a given probability spectrum, instantiated anew at each cycle. Hence the location of the source as well as the location of targets in relation to each other are irrelevant.
Reducing the probability levels of source and targets lengthens the time needed to reach any given activation level. At 100% it takes something like 3896 cycles until the first target element has reached level 9.
With source and target probabilities both set at 10%, it took 4927 cycles in this case to reach the same result. (Probability regions and % → Source → % = 10, Probability regions and % → Target → % = 10).
Using the same settings but now with 100 sources it took only 89 cycles to get to activation level 9. (Source elements → Number of source elements = 100).
Using the previous settings (100 sources, source and target probabilities 10%), but with Self-adjustment ON and Probability up/down step for sources and targets = 3, the cycling continues without activation level 9 being reached because with probabilities set at 10% the percentages for sources and targets are decremented until they reach 0. The sources become ineffective and the same goes for any targets which had been touched since Self-adjustment ON was ticked. Hence the Grid display appears to be static. Note the cycle number - 6518.
Clicking the Show regions button shows the source and target regions and their members, the probability levels for the sources are at 0, and some of the percentages for the targets have remained at 10 because they had not been touched since Self-adjustment ON was selected.
If Reverse ON for both sources and targets is ticked, the probability levels below 50% will be raised and by cycle 6596 we already have a target that has reached activation level 9.
Inspecting the regions we see the probabilities for the regions having settled at 51% since they increased when below the 50-mark but then were decremented back towards 50% as soon as they went further. The percentages for the targets vary because not all of them had been affected in the meantime.
Note: although the following screenshots do not show the Settings window with tabs, the Grid-related functionality is exactly the same as in the current version.
With different settings (see below, gaps between units drawn) it took 819 cycles in this case for one target to reach activation level 9.
Note the larger number of targets with activation level still at 0, while those that did receive (and from then on were capable of sending) nevertheless achieved reasonable activation levels. (Changing the settings and then reloading the file will revert the state of the system to the point when the file was last saved)
Since the probabilities for target region 3 were set at Self-adjustment ON and Probability up/down step = 10, the targets in region 3 have reached a probability level of 100% since they were incremented during the ensuing cycles.
Since the sources as well as many targets are more effective, by cycle 436 there is a target with activation level 9.
The settings are as follows:
By cycle 2236 there are 794 targets which have achieved an activation level of 3. At the beginning the current number of elements at that level were slow in appearing, their numbers rising more rapidly as time went on. Eventually their numbers are increasing at a steady rate.
Grouping the sources and/or the targets allows us observe the influence one region has in comparison to another. It also demonstrates the interdependency of the entire system. While the targets depend on the initial seeding, the chances for any one of them becoming more influential as its activation level had reached a critical point have risen after an initial slow start. From then onwards the probability levels become less significant due to the mutual relationships emerging between sending targets and their recipients.
Elements are only effective if they have hit upon a target. Those targets are candidates for sending, thereby adding to the pool of potential senders, and creating recipients in turn. Changing the probability levels of one or the other region during the cycles can break such patterns if their decremental and/or incremental steps are sufficient to affect those they come into contact with.
Hence there is a time lag between such causes and their effects, during which new patterns of dependencies can emerge that in turn direct the ongoing results.
At smaller scales (ie, small number of units) the cause and effect relationships in terms of higher and lower probabilities more or less hold; the number of cycles taken to achieve given activation levels are in line with the expectations. However, at larger scales groups of elements form that begin to define the probabilistic potential of their members away from the overall parameters. Even without an input from the sources (if their probabilities have been reduced to 0) such target groups are now capable of influencing their surrounds regardless. The result can be a run-away condition.
The equivalent in the real would be a scenario during which an initial influence had produced effects which, if unchecked, proliferate the effects from a certain point onwards where the sources are no longer needed; neutralising them is useless. All the while the identification of any particular cause and its effect remains impossible; trying to hunt them down is a waste of resources.
Note that in complex, dynamic systems the same applies to functionalities, in other words, types of behaviour which after all represent an aggregate form of causes. If a certain type of behaviour produces effects which are allowed to spread their influence through the system, disregarding the effects and/or the causes can also lead to a run-away condition in terms of the system's overall potential, even if the destructive elements are removed eventually (an example in society would be the detrimental effect caused by unmitigated authoritarian measures; the society collapses in the end).
Footnote: A true-to-life simulation of complex, dynamic systems requires algorithms which allow the emergence of states as the system goes through its paces, a bottom-up approach. The AI programs on this site are of that type. By contrast, linear simulations (and interpretations of complex, dynamic systems under essentially linear auspices) incorporate a top-down approach, that is there are pre-established parameters which define the system from the outset. They reflect reality to a certain degree but only insofar as the initial settings align with the real-life situation. The larger the system and the more influential the system's environment (that which is not part of the current focus), the less accurate the simulation will be.
CauseF is somewhere in the middle. While the outcomes on the screen are a result of emerging states, the probability values are still set by the user. In real life they also would define themselves along the system's time line, although there are boundaries which equally emerge alongside (see The mechanics of chaos: a primer for the human mind how they come into being).
A considerable range of software is available making use of the top-down approach as described above. One list can be found at List of system dynamics software. One example, Lumina, offers solutions to a number of scenarios (see Case Studies on their home page). Or Consideo, creating relational maps based on one's interpretation of the significance of various factors impacting on a scenario, from sales models to personal satisfaction.