  In AC electrical systems, the power depends on the real power (P) due to
resistive elements and the reactive power (Q) due to the inductive and
capacitive elements, which are commonly studied by using phasor and scalar
methods. Thus, this paper focuses on applying the fractal Julia sets to observe
the topological properties related to the signs and magnitudes of the real and
reactive powers consumed or supplied by an electrical circuit. To perform this,
different power combinations were used to represent the fractal diagrams with
an algorithm that considers the mathematical model of Julia sets. The study
considers three type of loads: the first study considers the change of real
power when the reactive power is fixed; the second study deals with the change
of the reactive power when the real power is fixed; and finally, the third
study contemplates that both real and reactive powers change. Furthermore, the
fractal diagrams of the power in the four quadrants of the complex plane are
studied to identify the topological properties that each sign and magnitude
represent. A qualitative analysis of the diagrams helps to identify that the
complex power loads present some fractal graphic patterns, with respect to the
signs and magnitudes considered in the different quadrants of the complex
planes. The diagrams represented in the complex planes save a relation in the
forms and structure with other points studied, concluding that the power is
related to other figures in other quadrants. Thus, this result allows a new
study of the behavior of the power in an electrical circuit, showing a clear
relation of the different fractal diagrams that the Julia sets obtained.
