{
"cells": [
{
"cell_type": "markdown",
"id": "261d10af",
"metadata": {},
"source": [
"# Installation"
]
},
{
"cell_type": "markdown",
"id": "71b45751",
"metadata": {},
"source": [
"To set up the python environment, we will use Anaconda ( www.anaconda.com). Click the link and follow the instructions.\n",
"\n",
"\n",
"Once installed, search for the installed app, which should be called something like **Anaconda-Navigator**. Once *Navigator* starts, go to *Environments*, and *Search Packages*. Please check for the following packages:\n",
"- numpy\n",
"- scipy\n",
"- matplotlib\n",
"- notebook (jupyter notebook)\n",
"- numba\n",
"- uncertainties\n",
"- pybind11"
]
},
{
"cell_type": "markdown",
"id": "cbe261a4",
"metadata": {},
"source": [
"We will also need a text editor for python codes (in addition to jupyter notebooks). **Spyder** is part of Anaconda, and is very powerful editor. You can find it inside *Anaconda-Navigator*.\n",
"\n",
"But other editors of your choice are equally good (for example *emacs* or *Aquamacs* or *vim* or *vi*)"
]
},
{
"cell_type": "markdown",
"id": "f556e632",
"metadata": {},
"source": [
"Some examples to speed up the code will be given in C++. It is not essential to have it, but you will learn more if you can set up the environment with a C++ compiler (such as gcc), which can be combined with Python. For installation instructions, see the `Optional installation of C++` below. We will also show examples below."
]
},
{
"cell_type": "markdown",
"id": "bec6c2f1",
"metadata": {},
"source": [
"We will test the installation with an excercise of plotting **Mandelbrot set.**"
]
},
{
"cell_type": "markdown",
"id": "22f41c3b",
"metadata": {},
"source": [
"## Mandelbrot set"
]
},
{
"cell_type": "markdown",
"id": "ab9d4c3d",
"metadata": {},
"source": [
"Wikipedia: The Mandelbrot set $M$ is defined by a family of complex quadratic polynomials $f(z) = z^2 + z_0$ where $z_0$ is a complex parameter. For each $z_0$, one considers the behavior of the sequence $(f(0), f(f(0)), f(f(f(0))), · · ·)$ obtained by iterating $f(z)$ starting at $z=0$, which either escapes to infinity or stays\n",
"within a disk of som finite radius. The *Mandelbrot set* is defined as the set of points $z_0$, such that the above sequence does not escape to infinity."
]
},
{
"cell_type": "markdown",
"id": "f6cadfbb",
"metadata": {},
"source": [
"More concretely, the sequence is : $(z_0,z_0^2+z_0,z_0^4+2 z_0^3+z_0^2+z_0,...)$.\n",
"\n",
"For large $z_0$ it behaves as $z_0^{2n}$ and clearly diverges at large $n$. Consequently, large $z_0$ is not part of the set. \n",
"\n",
"For small $z_0$, it is of the order of $z_0+O(z_0^2)$, and is small when $z_0$ is small. Such $z_0$ are part of the set.\n",
"\n",
"To determine that certain $z_0$ is not part of the *Mandelbrot set*, we check if $|f(f(f(....)))|>2$. \n",
"This treshold is sufficient, because the point with the largest magnitude that is still in the set is -2. Indeed, if we set $z_0=-2$, we see that $f(f(0))=(-2)^2-2=2$ and $f(f(f(0)))=2^2-2=2$, and for any number of itterations the sequence remains equal to $2$. Such sequence remains finite, and by definition $z_0=-2$ is part of the set, and $f(f(f(...)))=2$ might lead to finite sequence. \n",
"\n",
"For any other point $z_0\\ne -2$, we can show that once $f(f(f(...)))$ becomes $2$, it will lead to diverging sequence. For example, for $z_0=1$ we have $f(f(0))=2$ and $f(f(f(0)))=5$, and clearly grows.\n",
"\n",
"We will make density plot, with $Re(z_0)$ on $x$-axis, and $Im(z_0)$ on $y$-axis, and color will denote how long it took for the sequence to have absolute value equal to 2. The mandelbrot set will have one color, and all other colors \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "1338f8ce",
"metadata": {},
"outputs": [],
"source": [
"from numpy import * # because arrays are defined in numpy\n",
"\n",
"def Mand(z0, max_steps):\n",
" z = 0j # no need to specify type. \n",
" # To initialize to complex number, just assign 0j==i*0\n",
" for itr in range(max_steps):\n",
" if abs(z)>2:\n",
" return itr\n",
" z = z*z + z0\n",
" return max_steps\n",
"\n",
"\n",
"def Mandelbrot(ext, Nxy, max_steps):\n",
" \"\"\"\n",
" ext[4] -- array of 4 values [min_x,max_x,min_y,max_y]\n",
" Nxy -- int number of points in x and y direction\n",
" max_steps -- how many steps we will try at most before we conclude the point is in the set\n",
" \"\"\"\n",
" data = zeros((Nxy,Nxy)) # initialize a 2D dynamic array\n",
" for i in range(Nxy):\n",
" for j in range(Nxy):\n",
" x = ext[0] + (ext[1]-ext[0])*i/(Nxy-1.)\n",
" y = ext[2] + (ext[3]-ext[2])*j/(Nxy-1.)\n",
" # creating complex number of the fly\n",
" data[i,j] = Mand(x + y*1j, max_steps) \n",
" return data\n",
"# data now contains integers. \n",
"# MandelbrotSet has value 1000, and points not in the set have value <1000."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "07e8719a",
"metadata": {},
"outputs": [],
"source": [
"data = Mandelbrot([-2,1,-1,1], 500, 1000)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "17549e0a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
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