Periodical cicadas consist of broods with life cycles of either 13 or 17 years. Both life cycle values are prime numbers. Theorists in evolutionary biology have suggested that a benefit of prime-valued life cycles is they minimize overlap (or coincidence) with the life cycles of predators and of other cicada broods.
Prime Coincidence is a visualization of coincidence among prime-valued cycles, operating at one cycle per second. The dots shown in each cycle are colored to indicate a common period. For instance, all the dots that appear once every 7 cycles might be colored blue. The dots of a given color always appear in the same fixed positions in the grid, and no other dots can occur in those positions even on cycles when that color is not present. Every location in the grid is associated with a single dot color.
In the visualization shown here, dots follow one of 10 possible periods, consisting of the first 10 ascending prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So, the most frequently-occurring dot color appears every 2nd cycle, and the second-most frequent appears every 3rd cycle. The least-frequently occurring dot color appears only every 29 cycles. In this visualization, the number of dots of a given color is proportional to their period: That is, higher-period dot colors that appear less frequently are more numerous when they do appear, and lower-period dot colors that appear more frequently are less numerous.
In the special case of prime-numbered periods, we can calculate the period of coincidence of two different dot colors simply by multiplying their periods. For example, if blue dots appear every 7 cycles, and red dots appear every 11 cycles, then blue and red dots will both appear together (i.e., coincide) every 7 x 11 = 77 cycles.
The same math applies for calculating the coincidence of three or more dot colors: Just multiply their individual period values and you will find the period of their coincidence. In this way, we can calculate how many cycles we would need to wait for all 10 dot colors to appear simultaneously in a single cycle:
2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29 = 6,469,693,230
In other words, approximately once every 6.5 billion cycles. At one cycle per second, we would need to wait over 200 years for all 10 “broods” (dot colors) to appear at once.