Dive into NumPy! Start organizing, rearranging, and sampling your data.

Python Data Analysis and Visualization

From Python to Numpy

>**Note:**
You should look at the [ufunc.reduceat](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ufunc.reduceat.html) method that performs a (local) reduce with specified slices over a single axis.

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### Problem Description

We now want to measure the fractal dimension of the Mandelbrot set using the [Minkowski–Bouligand dimension](https://en.wikipedia.org/wiki/Minkowski%E2%80%93Bouligand_dimension). To do that, we need to do box-counting with a decreasing box size (see figure below). As you can imagine, we cannot use pure Python because it would be way too slow. The goal of the exercise is to write a function using NumPy that takes a two-dimensional float array and returns the fractal dimension. We'll consider values in the array to be normalized (i.e. all values are between 0 and 1).

Given below is the Minkowski-Bouligand dimension:

>**Note:**
You should look at the [ufunc.reduceat](https://docs.scipy.org/doc/numpy/reference/generated/numpy.ufunc.reduceat.html) method that performs a (local) reduce with specified slices over a single axis.

$$$$

# Problem Description

We now want to measure the fractal dimension of the Mandelbrot set using the [Minkowski–Bouligand dimension](https://en.wikipedia.org/wiki/Minkowski%E2%80%93Bouligand_dimension). To do that, we need to do box-counting with a decreasing box size (see figure below). As you can imagine, we cannot use pure Python because it would be way too slow. The goal of the exercise is to write a function using NumPy that takes a two-dimensional float array and returns the fractal dimension. We'll consider values in the array to be normalized (i.e. all values are between 0 and 1).

Given below is the Minkowski-Bouligand dimension:

This problem is an extension of the previous case study. In this lesson, we'll learn how to find the fractal dimension of the Mandelbrot set. 

Introduction

Anatomy of an Array

Code Vectorization

Problem Vectorization

Custom Vectorization

Beyond NumPy

Coding Example: Minkowski-Bouligand Dimension

Problem Description