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Figure 6 | Theoretical Biology and Medical Modelling

Figure 6

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

Figure 6

Calculations of the scale-invariant power law coefficient of the Koch curve using the CSSM method. The linear regression of the logarithm of the inverse of the steps (log(1/h)) is plotted against the logarithm of the root of the number of the points on the Koch curve to the absolute value of the determinant of the basic square matrix . Plot A: presents scale 4 (10-4) where the 0th, 1st, 2nd, 3rd and 4th orders consist of 2, 5, 17, 65, 257 and 1025 points, respectively. B and C present the other two scales: 10-5 and 10-6. The linear regression analyses of the plots are as follows: y = -41.44-15.187x (standard error = 2.36, correlation coefficient = 0.98), y = -73.81-19.81x (standard error = 5.02, correlation coefficient = 0.96), y = -134.43-27.77x (standard error = 5.45 and correlation coefficient = 0.98) for the A, B and C plots. D: presents the logarithms of the scales (log(scale)) plotted against the logarithms of the absolute values of the b coefficients (log|b scale |) in the regression line for the data plotted in figure 3 (A, B, C and D). The regression line has a slope equal to zero as it is presented in a linear regression (y = 0.017-0.26x: standard error = 0.12, correlation coefficient = 0.98).

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