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COMPLEXITY & ENTROPY AS FUNCTIONS OF STRUCTURE Five linear ( deterministic ) systems with increasing sizes ( structure ) were analyzed and the resulting values are shown . Lower and Current Complexities are the same hence Robustness is 100% in all cases.
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COMPLEXITY & ENTROPY AS A FUNCTION OF STRUCTURE Example worksheet representing a 20 variable linear system with 20 samples , used in the analysis Typical correlation found between variables in such deterministic systems
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COMPLEXITY, ROBUSTNESS & ENTROPY AS FUNCTIONS OF UNCERTAINTY Uncertainty ( see note) was gradually added to a 10x10 system. Current Complexity peaking and sudden robustness decrease are clearly visible in the imminence of system collapse . Note: Uncertainty is defined here as a LIMIT to a random value which is added to the respective cell of the linear system Excel worksheet, as in the formula: CellValue = CellValueFromLinearWorksheet + (LIMIT * RANDOM())
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Otherwise linear 10x10 systems, here affected by different uncertainties , are shown below along with typical correlations found in each instance . COMPLEXITY, ROBUSTNESS & ENTROPY AS FUNCTIONS OF UNCERTAINTY UNCERTAINTY 1 UNCERTAINTY 10