{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "148b2bdb-ecad-4491-a472-84640574f09d",
   "metadata": {},
   "source": [
    "# Homework 3\n",
    "\n",
    "Please run the following code cell first.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47134c36-6590-4ac8-85c6-d6bdfadb4600",
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots, TestImages, ImageShow\n",
    "\n",
    "img1 = testimage(\"chelsea\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4f1c303-2247-4507-a8ed-9d5a66f892d5",
   "metadata": {},
   "source": [
    "Images in Julia are just matrices of colors, e.g. of type `Matrix{Gray}` or `Matrix{RGB}`. \n",
    "\n",
    "Indices also run like in a matrix. So, `img1[1, 1]` is the pixel in the upper left corner and `img1[end, 1]` is the pixel in the lower left corner. \n",
    "\n",
    "## Exercise 1\n",
    "\n",
    "Write a function `my_crop(img)` that takes an image and returns the right half of it. If the image contains an uneven number of columns, include the center column. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b11a44ec-8553-4e52-99a7-278a2547ebb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "function my_crop(img)\n",
    "    # TODO: write the function\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acf109b6-61c4-4e7d-bec9-ebf603e21953",
   "metadata": {},
   "source": [
    "Test your function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "410db80c-5d07-49c0-8a65-d7d240cd0fbd",
   "metadata": {},
   "outputs": [],
   "source": [
    "my_crop(img1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01d85b43-6090-43b9-b720-2e2b4a8dafce",
   "metadata": {},
   "source": [
    "## Exercise 2\n",
    "\n",
    "Write a function `my_crop(img, margin)` that crops the image where margin is a number giving the percent of the width/height which is to be cropped on all 4 sides. So, `my_crop(img, 12)` should cut off 12% of the width on the right and left sides and 12% of the height on the top and bottom, respectively. \n",
    "\n",
    "You may use `round(Int,x)` to round a float `x` to the nearest integer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ebe624f-7fba-438c-b85f-2b9b16bd4ca1",
   "metadata": {},
   "outputs": [],
   "source": [
    "function my_crop(img, margin)\n",
    "   # TODO: write the function\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec805ad6-3451-42ea-8980-8f51e0d4bd2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Test it!\n",
    "img2 = my_crop(img1, 14)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbdb5a8c-becc-4e92-90b8-9901fd110da0",
   "metadata": {},
   "source": [
    "## Complex numbers in Julia \n",
    "\n",
    "The imaginary unit $i=\\sqrt{-1}$ is called `im` in Julia. Adding `+0im` to a real makes it complex. The `Complex` data type is - similar to the `Rational` data type - internally realised as a pair (real part, imaginary part) of numbers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "13dde679-1581-4445-90ef-47df35f62f9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0 + 1.4142135623730951im, -1.0 - 1.2246467991473532e-16im, Complex{Int64})"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sqrt(-2+0im), exp(-π*im), typeof(-1+2im)"
   ]
  },
  {
   "attachments": {
    "76160761-900d-4c5a-a295-f85379041eca.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "12208879-5a95-4a1b-888b-93a9b205e6f4",
   "metadata": {},
   "source": [
    "## Exercise 3 - Image of a Julia Set\n",
    "\n",
    "[Julia sets](https://de.wikipedia.org/wiki/Julia-Menge) (named after the mathematician Gaston Julia) describe the behaviour of iterative function application in the complex plane $\\mathbb{C}$. \n",
    "\n",
    "Let $c\\in\\mathbb{C}$ be some chosen complex number. Consider the map $f\\colon z \\mapsto z^2+c$. We study the behaviour of the sequence $z, f(z), f(f(z)), f(f(f(z))),...$. \n",
    "\n",
    "Depending on the starting value $z\\in\\mathbb{C}$, this sequence may remain in a bounded domain or grow without limits.\n",
    "\n",
    "By colour-coding the grow rate for different $z$ values we can generate nice fractal pictures. \n",
    "\n",
    "Your task is to implement the following pseudocode as an actual Julia function:\n",
    "\n",
    "\n",
    "![image.png](attachment:76160761-900d-4c5a-a295-f85379041eca.png)\n",
    "\n",
    "\n",
    "Test it by calculating the matrix `A` with the following input parameters:\n",
    "\n",
    "- $x$ is a vector of 1500 evenly spaced numbers from -1.5 to 1.5.\n",
    "- $y$ is a vector of 1000 evenly spaced numbers from -1 to 1.\n",
    "- $c = -0.4 + 0.61\\cdot i$\n",
    "- $R = 3$\n",
    "- $N = 1000$\n",
    "\n",
    "and plot the matrix $A$ with the function `jplot()` defined below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ed40aab5-3aa6-437f-a3fa-d870b37cfab5",
   "metadata": {},
   "outputs": [],
   "source": [
    "function juliaset(x,y,K,L,c,R,N)\n",
    "    A = zeros(K, L)\n",
    "\n",
    "    # TODO: complete the function\n",
    "    \n",
    "    return A\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a848e8b0-7ae8-478d-a97e-3727b1bee727",
   "metadata": {},
   "outputs": [],
   "source": [
    "jplot(A) = heatmap(A; \n",
    "    colormap = :viridis,\n",
    "    clims = (0, 0.15),\n",
    "    axis = :none,\n",
    "    ticks = :none,\n",
    ")\n",
    "L = 1500\n",
    "K = 1000\n",
    "c = -0.4 + 0.61*im\n",
    "x = range(-1.5, 1.5; length = L)\n",
    "y = range(-1.0, 1.0; length = K);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab6fc3be-dc87-4d28-af8c-1b91e94f4621",
   "metadata": {},
   "outputs": [],
   "source": [
    "# and now the test...\n",
    "\n",
    "A = juliaset(x, y, K, L, c, 3, 1000)\n",
    "jplot(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f6d7e67-c562-46c4-8982-b79a673b9ba8",
   "metadata": {},
   "source": [
    "Try other $c$ values,  e.g., $c=0.285+0.01\\cdot i$, $\\quad  c=−0.8+0.156\\cdot i$, $\\quad c=−0.835−0.2321\\cdot i$"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.13",
   "language": "julia",
   "name": "julia-1.13"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.13.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
