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Table 3 Koch curve orders and the related parameters used in calculating the scale-invariant power law coefficient using CSSM.

From: Self-organization of developing embryo using scale-invariant approach

Order # of Points at each order Scale Logarithm (Scale) b-coefficient of linear regression Logarithm of absolute b-coefficient
0 2 10-1 -1 -2.1323166 0.328851688
1 5 10-2 -2 -3.1527369 0.49868773
2 17 10-3 -3 -8.6691842 0.937978231
3 65 10-4 -4 -15.187111 1.181475167
4 257 10-5 -5 -19.809067 1.296864021
5 1025 10-6 -6 -27.767092 1.44353039
  1. The number of the orders, principal points and scales used in calculating the SIPL coefficient of the Koch curve using the zero centro-axial skew-symmetrical matrix method and the b-coefficients of the regression lines are presented in this table. The data are plotted between the logarithms of the nth root of the absolute value of the basic square matrix at the order (where n is the number of principal points) and the logarithms of the inverse of step(log(1/h)). The logarithms of the absolute b-coefficients are plotted against the logarithms of the scales. The calculations of the regression line of this plot were used in calculating the scale-invariant power law coefficient of the Koch curve.