Project-Fern-I.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project: Fern"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theory (source: [Wikipedia [1]](https://en.wikipedia.org/wiki/Barnsley_fern))\n",
    "\n",
    "**The first point** drawn is at the origin (x0 = 0, y0 = 0) and then the new points are iteratively computed by randomly applying one of the following four coordinate transformations:[4][5]\n",
    "\n",
    "ƒ1\n",
    "\n",
    "    xn + 1 = 0\n",
    "    yn + 1 = 0.16 yn.\n",
    "\n",
    "This coordinate transformation is chosen 1% of the time and just maps any point to a point in the first line segment at the base of the stem. This part of the figure is the first to be completed during the course of iterations.\n",
    "\n",
    "\n",
    "ƒ2\n",
    "\n",
    "    xn + 1 = 0.85 xn + 0.04 yn\n",
    "    yn + 1 = −0.04 xn + 0.85 yn + 1.6.\n",
    "    \n",
    "This coordinate transformation is chosen 85% of the time and maps any point inside the leaflet represented by the red triangle to a point inside the opposite, smaller leaflet represented by the blue triangle in the figure.\n",
    "\n",
    "ƒ3\n",
    "\n",
    "    xn + 1 = 0.2 xn − 0.26 yn\n",
    "    yn + 1 = 0.23 xn + 0.22 yn + 1.6.\n",
    "    \n",
    "This coordinate transformation is chosen 7% of the time and maps any point inside the leaflet (or pinna) represented by the blue triangle to a point inside the alternating corresponding triangle across the stem (it flips it).\n",
    "\n",
    "ƒ4\n",
    "\n",
    "    xn + 1 = −0.15 xn + 0.28 yn\n",
    "    yn + 1 = 0.26 xn + 0.24 yn + 0.44.\n",
    "    \n",
    "This coordinate transformation is chosen 7% of the time and maps any point inside the leaflet (or pinna) represented by the blue triangle to a point inside the alternating corresponding triangle across the stem (without flipping it).\n",
    "\n",
    "The first coordinate transformation draws the stem. The second generates successive copies of the stem and bottom fronds to make the complete fern. The third draws the bottom frond on the left. The fourth draws the bottom frond on the right. The recursive nature of the IFS guarantees that the whole is a larger replica of each frond. Note that the complete fern is within the range −2.1820 < x < 2.6558 and 0 ≤ y < 9.9983."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fern can be created by implementation of ```if loops``` and ```while loop```. We will discuss three different approaches to create fern."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1: Direct implementation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import random as random\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1 Create Fern Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "logfile = open(\"data/log.txt\",'w')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "'''initialize first coordinate'''\n",
    "x = 0\n",
    "y = 0\n",
    "\n",
    "'''create list to hold x and y coordinates'''\n",
    "X = [x]\n",
    "Y = [y]\n",
    "\n",
    "'''initialize t for iteration'''\n",
    "t=1\n",
    "\n",
    "'''set itration number'''\n",
    "ITR = 100000\n",
    "\n",
    "'''set 'isprint' boolean variable to print in logfile/terminal'''\n",
    "isprint = True\n",
    "\n",
    "'''control datapoints with while loop'''\n",
    "while t < ITR:\n",
    "    \n",
    "    '''generate a random variable'''\n",
    "    r = random.uniform(0,100)\n",
    "    \n",
    "    '''condition-I'''\n",
    "    if r <  1.0:\n",
    "        x = 0\n",
    "        y = 0.16*Y[t-1]\n",
    "        X.append(x) ; Y.append(y)\n",
    "        \n",
    "        '''condition-II'''    \n",
    "    elif r > 1.0 and r < 86.0:\n",
    "        x = 0.85*X[t-1] + 0.04*Y[t-1]\n",
    "        y = -0.04*X[t-1] + 0.85*Y[t-1]+1.6\n",
    "        X.append(x);Y.append(y)\n",
    "        \n",
    "        '''condition-III'''    \n",
    "    elif r > 86.0 and r < 93.0:\n",
    "        x = 0.2*X[t-1] - 0.26*Y[t-1]\n",
    "        y = 0.23*X[t-1] + 0.22*Y[t-1] + 1.6\n",
    "        \n",
    "        X.append(x);Y.append(y)\n",
    "    \n",
    "        '''condition-IV'''\n",
    "    elif r > 93.0 and r < 100.0:\n",
    "        x = -0.15*X[t-1] + 0.28*Y[t-1]\n",
    "        y = 0.26*X[t-1] + 0.24*Y[t-1] + 0.44\n",
    "        \n",
    "        X.append(x);Y.append(y)\n",
    "        \n",
    "        \n",
    "    if isprint:\n",
    "        #print(\"step: \",t,\"random number is: \", r,\\\n",
    "        #                \"coordinate is : \", x,y)\n",
    "        \n",
    "        logfile.write(\"step: \" + str(t) + \" random number is: \" + str(r) + \\\n",
    "                         \" coordinate is : \" + str(x) + \",\"+str(y))\n",
    "        \n",
    "        logfile.write(\"\\n\")\n",
    "        \n",
    "        \n",
    "    t = t+1\n",
    "    \n",
    "logfile.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2 Save data to a Json file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "Data = {\"x\":X,\"y\":Y}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json as json\n",
    "with open(\"data/fern_dictionary.json\",'w') as f:\n",
    "    json.dump(Data,f)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3 Create a Dataframe and save data as csv file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.064000</td>\n",
       "      <td>2.960000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.172800</td>\n",
       "      <td>4.113440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.311418</td>\n",
       "      <td>5.089512</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0  0.000000  0.000000\n",
       "1  0.000000  1.600000\n",
       "2  0.064000  2.960000\n",
       "3  0.172800  4.113440\n",
       "4  0.311418  5.089512"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DF = pd.DataFrame(Data)\n",
    "DF.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "DF.to_csv('data/fern_dataframe.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4 Create a Plot and save it as png/pdf file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = [5,9])\n",
    "plt.scatter(X,Y,color = 'g',marker = '.')\n",
    "plt.savefig(\"plot/fern.pdf\")\n",
    "plt.savefig(\"plot/fern.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mini Assignment\n",
    "- Define random walk in 2D\n",
    "- Create a random walk data and save data to file (json/csv)\n",
    "- Create a plot for random walk in 2D as save the plot as (pdf/png) file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Hint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''if you are in (xi,yi) position go to (xf,yf)'''\n",
    "\n",
    "'''set up xi,yi'''\n",
    "<TO DO>\n",
    "\n",
    "'''store x and y into X and Y list'''\n",
    "<TO DO>\n",
    "\n",
    "''' iterate to N steps using for loop'''\n",
    "<TO DO>\n",
    "        direction =  random.choice(['x','y'])\n",
    "        if direction == 'x':\n",
    "            r = random.choice([-1,1])\n",
    "            x = X[t-1] +rx\n",
    "            y = Y[t-1]\n",
    "        if direction == 'y':\n",
    "            r = random.choice([-1,1])\n",
    "            y = Y[t-1] + ry\n",
    "            x = X[t-1]\n",
    "    \n",
    "        '''remember to update X and Y in every loop'''\n",
    "        X.append(x)\n",
    "        Y.append(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reference:\n",
    "[1] [Barnsley fern](https://en.wikipedia.org/wiki/Barnsley_fern)"
   ]
  }
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