#### Overview of this book

Today's world of science and technology is all about speed and flexibility. When it comes to scientific computing, NumPy is on the top of the list. NumPy will give you both speed and high productivity. "NumPy Cookbook" will teach you all about NumPy, a leading scientific computing library. NumPy replaces a lot of the functionality of Matlab and Mathematica, but in contrast to those products, it is free and open source. "Numpy Cookbook" will teach you to write readable, efficient, and fast code that is as close to the language of Mathematics as much as possible with the cutting edge open source NumPy software library. You will learn about installing and using NumPy and related concepts. At the end of the book, we will explore related scientific computing projects. This book will give you a solid foundation in NumPy arrays and universal functions. You will also learn about plotting with Matplotlib and the related SciPy project through examples. "NumPy Cookbook" will help you to be productive with NumPy and write clean and fast code.
Table of Contents (17 chapters)
NumPy Cookbook
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Free Chapter
Winding Along with IPython
Advanced Indexing and Array Concepts
Get to Grips with Commonly Used Functions
Connecting NumPy with the Rest of the World
Audio and Image Processing
Special Arrays and Universal Functions
Profiling and Debugging
Quality Assurance
Speed Up Code with Cython
Index

## Combining images

In this recipe, we will combine the famous Mandelbrot fractal (for more information on Madelbrot set visit http://en.wikipedia.org/wiki/Mandelbrot_set) and the image of Lena. These types of fractals are defined by a recursive formula, where you calculate the next complex number in a series by multiplying the current complex number you have, by itself and adding a constant to it.

### Getting ready

Install SciPy, if necessary. The See Also section of this recipe, has a reference to the related recipe.

### How to do it...

We will start by initializing the arrays, followed by generating and plotting the fractal, and finally, combining the fractal with the Lena image.

1. Initialize the arrays.

We will initialize `x`, `y`, and `z` arrays corresponding to the pixels in the image area with the `meshgrid`, `zeros`, and `linspace` functions:

```x, y = numpy.meshgrid(numpy.linspace(x_min, x_max, SIZE),
numpy.linspace(y_min, y_max, SIZE))
c = x + 1j * y
z = c.copy()
fractal = numpy.zeros(z.shape, dtype=numpy.uint8...```