  This paper presents discontinuous Riemann integrable functions on the unit
interval $[0, 1]$ derived from the dynamics of two-dimensional elementary
cellular automata. Based on the self-similarities of their orbits, we write
down the numbers of nonzero states in the spatial and spatio-temporal patterns
and obtain discontinuous Riemann integrable functions by normalizing the
values. We calculate the integrals of the two obtained functions over $[0, 1]$
and demonstrate the relationship between them.
