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We investigate two discrete models of excitable media on a one-dimensional integer lattice ℤ: the κ-color Cyclic Cellular Automaton (CCA) and the κ-color Firefly Cellular Automaton (FCA). In both models, sites are assigned uniformly random colors from ℤ/κℤ. Neighboring sites with colors within a specified interaction range r tend to synchronize their colors upon a particular local event of 'excitation'. We establish that there are three phases of CCA/FCA on ℤ as we vary the interaction range r. First, if r is too small (undercoupled), there are too many non-interacting pairs of colors, and the whole graph ℤ will be partitioned into non-interacting intervals of sites with no excitation within each interval. If r is within a sweet spot (critical), then we show the system clusters into ever-growing monochromatic intervals. For the critical interaction range r=⌊κ/2⌋, we show the density of edges of differing colors at time t is Θ(t−1/2) and each site excites Θ(t1/2) times up to time t. Lastly, if r is too large (overcoupled), then neighboring sites can excite each other and such 'defects' will generate waves of excitation at a constant rate so that each site will get excited at least at a linear rate. For the special case of FCA with r=⌊2/κ⌋+1, we show that every site will become (κ+1)-periodic eventually.