PMC

The relationship between number of neighbours and cell area: (A) symmetric cell division with isotropic growth; (B) asymmetric cell division with isotropic growth; (C) symmetric cell division with anisotropic growth value of 0·5; (D) asymmetric cell division with anisotropic growth value of 0·5; (E) symmetric cell division with anisotropic growth value of 1; (F) asymmetric cell division with anisotropic growth value of 1; (G) symmetric cell division with isotropic growth where cell division is restricted to the boundary cells; and (H) experimental data of Arabidopsis shoot apical meristem (SAM). Sym, symmetric; Asym, asymmetric; Symp, symmetric peripheral cells. Lewis' law equation, A_n = (n – 2)/4, is shown in red, where A_n is the mean normalized cell area and n is number of neighbours. The blue lines represent the affine fit of the data. Cell area is normalized by dividing the individual cell area by the mean of the cell areas in the tissue.

Area division between two identical agents. Yellow, blue and gray indicate the area assigned to the first UAV, the second UAV and unassigned, respectively. Image on the left shows a sub-optimal division where . Image in the middle shows a sub-optimal division because . Image on the right shows an optimal area division matching the conditions shown in Equation ().

Derivation of the formulae for the platelet division fraction. The number of platelets (red or green) counted by microscopic observation equals the original input of platelets (R₀ or G₀) plus the newly generated platelets (platelet division: F_rR₀ or F_gG₀; Equations (1) and (2). Because the red-green doublets must have been formed by two platelets that happened to come into contact and not by division, the number of the happen-to-be red-red doublets can be calculated from their binomial coefficient relationship (Equation (3)). The observed number of red-red doublets equals the number of those happen-to-be red-red doublets plus the doublets formed by division (F_rR₀; Equation (4)). By replacing R₀ and G₀ in Equations (4) and (5) with those in Equations (1) and (2), the fractions of platelet division (F_r and F_g) can be expressed by the variables with known values. The variables with unknown values are written here in magenta.

Chromosome division. The distribution of C_d (chromosome division, Equation 10) based on [S₁, S₂]^ML pairs for the 326 chromosomes indicated in the text. C_d is plotted along the X axis and represents the deviation from equal chromosome division.