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Table 1
Theoretically predicted occurrence frequency distribution powerlaw slopes α and power indices β of parameter correlations predicted for SOC cellular automatons with Euclidean space dimensions S = 1,2,3.
| Parameter | Theory | S = 1 | S = 2 | S = 3 |
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| Fractal Dimension: | DS = (1 + S)/2 | 1 | 3/2 | 2 |
| Length scale powerlaw slope: | αL = S | 1 | 2 | 3 |
| Duration powerlaw slope: | αT = (1 + S)/2 | 1 | 3/2 | 2 |
| Instantaneous energy dissipation rate slope: | αF = 1 + (S − 1)/DS | 1 | 5/3 | 2 |
| Peak energy dissipation rate slope: | αP = 2 − 1/S | 1 | 3/2 | 5/3 |
| Energy powerlaw slope: | αE = 1 + (S − 1)/(DS + 2) | 1 | 9/7 | 3/2 |
| Diffusive scaling of length L with duration T, | L ∝ T1/2 | L ∝ T1/2 | L ∝ T1/2 | L ∝ T1/2 |
| Correlation of peak rate F with duration T, | F ∝ TDS/2 | F ∝ T1/2 | F ∝ T3/4 | F ∝ T1 |
| Correlation of peak rate P with duration T, | P ∝ TS/2 | P ∝ T1/2 | P ∝ T1 | P ∝ T3/2 |
| Correlation of energy E with duration T, | E ∝ T1 + DS/2 | E ∝ T3/2 | E ∝ T7/4 | E ∝ T2 |
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