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Description

A plain render, showing the possible density of the Mandelbrot set!

(Please enlarge the image, to see it's full beauty).

Realized using Imagina (One of the fastest Mandelbrot set explorers).

Theoretical, this image requires a BUNCH of iterations (Imagina has choosen 4077058560 iterations), but the time required for this image was around 7 ~ 8 minutes.

This is because of the following humongous algorithms: Perturbation and Linear Approximation.

Perturbation makes it possible to use plain "naive" floating point numbers for the computation, which is much faster, than using a arbitrary precision datatype (like GMP or MPFR numbers).

Linear approximation truncates the number of required iterations from (for example) 4,077,058,560 to 20,000 iterations, using a precision and radius condition, because it is possible to skip some iterations, without manipulating the final result

(the image).

Description

A plain render, showing the possible density of the Mandelbrot set!

(Please enlarge the image, to see it's full beauty).

Realized using Imagina (One of the fastest Mandelbrot set explorers).

Theoretical, this image requires a BUNCH of iterations (Imagina has choosen 4077058560 iterations), but the time required for this image was around 7 ~ 8 minutes.

This is because of the following humongous algorithms: Perturbation and Linear Approximation.

Perturbation makes it possible to use plain "naive" floating point numbers for the computation, which is much faster, than using a arbitrary precision datatype (like GMP or MPFR numbers).

Linear approximation truncates the number of required iterations from (for example) 4,077,058,560 to 20,000 iterations, using a precision and radius condition, because it is possible to skip some iterations, without manipulating the final result

(the image).