Figure 1

Time decay of the order parameters at criticality for the PCPD rule $\mathsf{p}\mathsf{p}12$ ($p_{\mathrm{c}}=0.795410[5]$) in logarithmic scales. Single run on a system of $2^{22}$ sites, starting from two particles on each site (other initial conditions do not influence the asymptotic behavior). Different order parameters, from top to bottom: density of particles, density of pairs (e.g., by summing all particles of sites occupied by at least 2), fraction of occupied sites, and fraction of sites occupied by at least a pair. Inset: same, but for order parameters multiplied by $t^{0.2}$.Reuse & Permissions

Figure 2

Time decay of the total density of particles at criticality for various TCPD rules in logarithmic scales. Single runs on a system of $2^{22}$ sites, starting from three particles on each site. From top to bottom: rule $\mathsf{t}\mathsf{t}11$, $p_{\mathrm{c}}=0.53948(1)$; rule $\mathsf{t}\mathsf{t}12$, $p_{\mathrm{c}}=0.72899(1)$; rule $\mathsf{t}\mathsf{t}13$, $p_{\mathrm{c}}=0.822055(3)$; rule $\mathsf{t}\mathsf{t}22$, $p_{\mathrm{c}}=0.61900(2)$; rule $\mathsf{t}\mathsf{t}33$, $p_{\mathrm{c}}=0.70323(2)$; Inset: same, but multiplied by $t^{0.27}$. All data have been shifted for clarity.Reuse & Permissions

Figure 3

Same as Fig. 2 but for hybrid rules $m>n$. From top to bottom: rule $\mathsf{t}\mathsf{p}12$, $p_{\mathrm{c}}=0.81156(1)$, $2^{24}$ sites; rule $\mathsf{t}\mathsf{s}21$, $p_{\mathrm{c}}=0.62121(2)$, $2^{20}$ sites; rule $\mathsf{t}\mathsf{p}22$, $p_{\mathrm{c}}=0.756625(5)$, $2^{22}$ sites; rule $\mathsf{p}\mathsf{s}11$, $p_{\mathrm{c}}=0.71529(1)$, $2^{20}$ sites. Inset: same, but multiplied by $t^{0.16}$.Reuse & Permissions

Figure 4

Same as Fig. 2 but for $\mathsf{p}\mathsf{t}xx$ hybrid rules. From top to bottom: rule $\mathsf{p}\mathsf{t}42$, $p_{\mathrm{c}}=0.56775(4)$; rule $\mathsf{p}\mathsf{t}22$, $p_{\mathrm{c}}=0.54640(2)$; rule $\mathsf{p}\mathsf{t}12$, $p_{\mathrm{c}}=0.33250(3)$; rule $\mathsf{p}\mathsf{t}13$, $p_{\mathrm{c}}=0.66210(2)$. Inset: same, but multiplied by $t^{0.2}$.Reuse & Permissions