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Python Data Analysis and Visualization

From Python to Numpy

> *Temporal vectorization* is where elements share the same computation but necessitate a different number of iterations.


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### Problem Description

**The Mandelbrot** set is the set of complex numbers $c$ for which
the function $f_c(z) = z^2+ c$ does not diverge when iterated
from $z=0$, i.e., for which the sequence $f_c(0), f_c(f_c(0)) $, etc., remains bounded in an absolute value. It is very easy
to compute, but it can take a very long time because you need to
ensure a given number does not diverge. This is generally done by
iterating the computation up to a maximum number of iterations, after
which, if the number is still within some bounds, it is considered
non-divergent.


Of course, the more iterations you do, the more
precision you get.



> *Temporal vectorization* is where elements share the same computation but necessitate a different number of iterations.


$$$$
# Problem Description

**The Mandelbrot** set is the set of complex numbers $c$ for which
the function $f_c(z) = z^2+ c$ does not diverge when iterated
from $z=0$, i.e., for which the sequence $f_c(0), f_c(f_c(0)) $, etc., remains bounded in an absolute value. It is very easy
to compute, but it can take a very long time because you need to
ensure a given number does not diverge. This is generally done by
iterating the computation up to a maximum number of iterations, after
which, if the number is still within some bounds, it is considered
non-divergent.


Of course, the more iterations you do, the more
precision you get.



This lesson explains temporal vectorization with an interesting case study called "Mandelbrot set".

Introduction

Anatomy of an Array

Code Vectorization

Problem Vectorization

Custom Vectorization

Beyond NumPy

Temporal Vectorization

Problem Description