I liked math classes in school and reading about other math topics like fractals and polyhedra.
This equation gives well known and pretty results when iterated on the complex plane with c being the complex number and z starting at 0 for each number c you use:
z = z^2 + c
and getting the results colored by your choice of coloring algorithm.
I built some paper polyhedra before, including the Platonic, Archimedean and Kepler-Poinsot solids.
----
Why is a number raised to 0 equal to 1?
See this: x^n / x^m. For example, make n = 5 and n = 3, so this is
x*x*x*x*x / x*x*x
The x's cancel out to leave x*x or x^2.
This is like writing x^5/x^3 = x^(5-3) = x^2.
What if n and m are the same? Make n=m=3 and we have
x*x*x / x*x*x
or x^3 / x^3
or x^(3-3) = x^0.
Since x^3 on the top is the same as x^3 on the bottom, it is one.
Generally:
x^0 = x^(n-n) = x^n / x^n = 1.
This equation gives well known and pretty results when iterated on the complex plane with c being the complex number and z starting at 0 for each number c you use:
z = z^2 + c
and getting the results colored by your choice of coloring algorithm.
I built some paper polyhedra before, including the Platonic, Archimedean and Kepler-Poinsot solids.
----
Why is a number raised to 0 equal to 1?
See this: x^n / x^m. For example, make n = 5 and n = 3, so this is
x*x*x*x*x / x*x*x
The x's cancel out to leave x*x or x^2.
This is like writing x^5/x^3 = x^(5-3) = x^2.
What if n and m are the same? Make n=m=3 and we have
x*x*x / x*x*x
or x^3 / x^3
or x^(3-3) = x^0.
Since x^3 on the top is the same as x^3 on the bottom, it is one.
Generally:
x^0 = x^(n-n) = x^n / x^n = 1.
