One of the first applications of a dol-system was to

Question

Question: One of the first applications of a DOL-system was to simulate the development of a fragment of a multicellular filament such as that found in the blue-green bacteria Anabena catenula and various algae. The symbols a and b can be used to represent the cytological states of the cells, i.e., their size and readiness to divide. Subscripts l and r will be used to indicate cell polarity, specifying the positions in which daughter cells of type a and b will be produced. The development is described by the following L-system:

ω: a_r

p_1: a_r → a_lb_r

p_2: a_l → b_la_r

p_3: b_r → a_r

p_4: b_l → a_l

Implement a DOL-system to simulate the development of Anabaena catenula, and list the sequence of words obtained in the first 10 generations. Knowing that under the microscope the filaments appear as a sequence of cylinders of various lengths, with e-type cells longer than b-type cells, draw a schematic image of filament development according to the result obtained with the DOL-system implemented. Hint: you can indicate the polarity of a cell with an arrow. For instance, an l polarity is indicated by a left arrow, and an r polarity is indicated by a right arrow.