L-systems define recursive replacement rules, which offer a solid way to build fractals. Parrondo’s paradox has been used in fractals and chaos to obtain alternate escape-time fractals and alternate chaotic attractors. This paper studies fractals produced by running two distinct L-systems in parallel. The objective is to examine the visual characteristics and patterns that result from this iterative process. The two utilized L-systems have different rewrite rules and characteristics but are based on popular fractal designs. Whereas the second L-system creates a design of a Sierpinski upside arrowhead curve pattern, the first L-system yields a pattern of such kind. Making the fractals involves applying the Sierpinski L-system several times in a row, followed by another application of the system multiple times, and then continuing this alternating process. The two L-system fractals interact to produce new hybrid designs, and the patterns get more complicated as the number of iterations increases. In this paper, we have given a tutorial on generating alternate mathematical fractals using an L-system. Koch Snowflake, Koch curve, Dragon curve, Sierpinski curve, etc., have been considered examples, and their alternate L-system models have been visualized.