A probabilistic process of infection and recovery generates a pattern seen on "textile" shells, and certain other kinds of sea shells. Each new row follows some infection-recovery rules. Each row is permanent, but the next row is a variant of the previous. This is a space-time plot or diagram.
Creates a row of square clones, some are red (imagine they are "infected"). Then the row "stamps" its color onto the backdrop. Then the row of clones moves down a row and follows a process of infection and recovery. At each time step, with a certain probability, the red "infection" spreads to the two susceptible neighbors on the right and left of the infected clone. After a clone is infected, that clone recovers and is immune for the next few time steps, after which the sprite returns to being susceptible to infection. At each time step the red from the infected sprites leaves a mark, or "stamp," on a the portion of backdrop behind it. The row of sprites moves down to the next row of patches. This process of sprites stamping on the patches (simulating a shell surface), leaves a permanent record (like a time-space diagram or plot), resulting in the type of patterns on certain shells. The percentage of clones recovering with immunity at each time step is a key part of the pattern formation. The code roughly simulates pattern formation on a growing shell. The model uses a single horizontal row of sprites to simulate cells that spread pigment. The sprites change color over time, move, and leave a permanent record of the color change on the shell. This process creates a pattern roughly as seen in certain Mollusc shells. I developed this as part of our Discovery Box on spots and stripes on shells and lizards, which includes a "textile" sea-shell with similar patterns.
