basis: julia-fractalz(0) = pixel; z(n + 1) = z(n)² + c 2 parameters: real and imaginary parts of c. These sets were named for mathematician Gaston
Julia, and can be generated by a
simple change in the iteration process described for the Mandelbrot
Set.Start with a specified value of C, "C-real + i * C-imaginary"; use as the initial value of Z "x-coordinate + i * y-coordinate"; and repeat the same iteration, Z(n+1) = Z(n)² + C. |
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The relationship between the Mandelbrot
set and Julia set can hold between other sets as well. All these
are generated by equations that are of the form z(k+1) = f[z(k),c],
where the function orbit is the sequence z(0), z(1), ..., and
the variable c is a complex parameter of the equation. The value c is fixed for "Julia" sets. The initial orbit value z(0) is the complex number corresponding to the screen pixel. |