This work is inserted in the context of technical high school and
it aimed to analyze the integration between the branches of Fractal
Geometry, Analytical Geometry and Computer Programming.
For this purpose, we carried out a bibliographic search about what
characterizes and distinguishes Fractal Geometry from Euclidean
Geometry, we also seek in our readings to list the most famous
fractals. Then, we developed (in python language) several fractal
generation programs. It was possible to work with amazing and
easily programmable fractal shapes, such as the Cantor Set, the
Hilbert Curve and Sierpinski Triangle. We also built two new families
of fractal shapes from a generalization of the Koch Curve. We
conclude that programming fractals in the context of technical high
school is productive and challenging, as it requires many changes
in the representations of fractal patterns.