Merge branch 'master' into stable_marriage_in_python

Author: Amaras

CONTRIBUTORS.md

@@ -42,10 +42,12 @@ This file lists everyone, who contributed to this repo and wanted to show up her
 - Christopher Milan
 - Vexatos
 - Raven-Blue Dragon
-- Björn Heinrichs 
+- Björn Heinrichs
 - Olav Sundfør
 - Ben Chislett
 - dovisutu
 - Antetokounpo
 - Akash Dhiman
+- Vincent Zalzal
+- Jonathan D B Van Schenck
 - Amaras

SUMMARY.md

@@ -4,6 +4,7 @@
 * [Introduction](contents/introduction/introduction.md)
 * [How To Contribute](contents/how_to_contribute/how_to_contribute.md)
 * [Plotting](contents/plotting/plotting.md)
+    * [Iterated Function Systems](contents/IFS/IFS.md)
 * [Data Structures](contents/data_structures/data_structures.md)
     * [Stacks and Queues](contents/stacks_and_queues/stacks_and_queues.md)
 * [Mathematical Background](contents/mathematical_background/mathematical_background.md)

contents/IFS/IFS.md

@@ -0,0 +1,65 @@
+#include <cmath>
+#include <fstream>
+#include <random>
+#include <vector>
+
+// Simple X-Y point structure, along with some operators
+struct Point {
+  double x, y;
+};
+
+Point operator+(Point lhs, Point rhs) { return {lhs.x + rhs.x, lhs.y + rhs.y}; }
+Point operator*(double k, Point pt) { return {k * pt.x, k * pt.y}; }
+Point operator*(Point pt, double k) { return k * pt; }
+
+using PointVector = std::vector<Point>;
+
+// Returns a pseudo-random number generator
+std::default_random_engine& rng() {
+  // Initialize static pseudo-random engine with non-deterministic random seed
+  static std::default_random_engine randEngine(std::random_device{}());
+  return randEngine;
+}
+
+// Returns a random double in [0, 1)
+double drand() {
+  return std::uniform_real_distribution<double>(0.0, 1.0)(rng());
+}
+
+// Returns a random integer in [0, numElems-1]
+std::size_t randrange(std::size_t numElems) {
+  return std::uniform_int_distribution<std::size_t>(0, numElems - 1)(rng());
+}
+
+// Return a random point from the non-empty PointVector
+Point choose(const PointVector& points) {
+  return points[randrange(points.size())];
+}
+
+// This is a function to simulate a "chaos game"
+PointVector chaosGame(int numOutputPoints, const PointVector& inputPoints) {
+  // Choose first point randomly
+  Point curPoint = {drand(), drand()};
+
+  // For each output point, compute midpoint to random input point
+  PointVector outputPoints(numOutputPoints);
+  for (auto& outPoint : outputPoints) {
+    outPoint = curPoint;
+    curPoint = 0.5 * (curPoint + choose(inputPoints));
+  }
+
+  return outputPoints;
+}
+
+int main() {
+  // This will generate a Sierpinski triangle with a chaos game of n points for
+  // an initial triangle with three points on the vertices of an equilateral
+  // triangle.
+  PointVector inputPoints = {{0.0, 0.0}, {0.5, std::sqrt(0.75)}, {1.0, 0.0}};
+  auto outputPoints = chaosGame(10000, inputPoints);
+
+  // It will output the file sierpinski.dat, which can be plotted after
+  std::ofstream ofs("sierpinski.dat");
+  for (auto pt : outputPoints)
+    ofs << pt.x << '\t' << pt.y << '\n';
+}

contents/IFS/code/c++/IFS.cpp

@@ -0,0 +1,29 @@
+using DelimitedFiles
+
+# This is a function to simulate a "chaos game"
+function chaos_game(n::Int, shape_points)
+
+    # Initializing the output array and the initial point
+    output_points = zeros(n,2)
+    point = [rand(), rand()]
+
+    for i = 1:n
+        output_points[i,:] .= point
+        point = 0.5*(rand(shape_points) .+ point)
+    end
+
+    return output_points
+
+end
+
+# This will generate a Sierpinski triangle with a chaos game of n points for an 
+# initial triangle with three points on the vertices of an equilateral triangle:
+#     A = (0.0, 0.0)
+#     B = (0.5, sqrt(0.75))
+#     C = (1.0, 0.0)
+# It will output the file sierpinski.dat, which can be plotted after
+shape_points = [[0.0, 0.0],
+                [0.5, sqrt(0.75)],
+                [1.0, 0.0]]
+output_points = chaos_game(10000, shape_points)
+writedlm("out.dat", output_points)

contents/IFS/code/julia/IFS.jl

@@ -0,0 +1,25 @@
+from random import random, choice
+from math import sqrt
+
+# This generator simulates a "chaos game"
+def chaos_game(n, shape_points):
+    # Initialize the starting point
+    point = [random(), random()]
+
+    for _ in range(n):
+        # Update the point position and yield the result
+        point = [(p + s) / 2 for p, s in zip(point, choice(shape_points))]
+        yield point
+
+# This will generate a Sierpinski triangle with a chaos game of n points for an
+# initial triangle with three points on the vertices of an equilateral triangle:
+#     A = (0.0, 0.0)
+#     B = (0.5, sqrt(0.75))
+#     C = (1.0, 0.0)
+# It will output the file sierpinski.dat, which can be plotted after
+shape_points = [[0.0, 0.0],
+                [0.5, sqrt(0.75)],
+                [1.0, 0.0]]
+with open("sierpinski.dat", "w") as f:
+    for point in chaos_game(10000, shape_points):
+        f.write("{0}\t{1}\n".format(*point))

contents/IFS/code/python/IFS.py

@@ -96,37 +96,37 @@ These operations are called *gates*, and follow somewhat straightforward logic.
 The *AND* gate, for example, reads in 2 bits and will only output a 1 value if both inputs are 1. This can be seen in the corresponding truth table:
 
 <p>
-    <img  class="center" src="res/and.jpg" width="423" />
+    <img  class="center" src="res/and.jpg" style="width:50%" />
 </p>
 
 The *OR* gate will output 1 if either input bits are 1:
 
 <p>
-    <img  class="center" src="res/or.jpg" width="423" />
+    <img  class="center" src="res/or.jpg" style="width:50%" />
 </p>
 
 The *exclusive OR* or *XOR* gate is the same as the *OR* gate, but will not output 1 if both bits are 1:
 
 <p>
-    <img  class="center" src="res/xor.jpg" width="423" />
+    <img  class="center" src="res/xor.jpg" style="width:50%" />
 </p>
 
 The *NOT* gate simply flips the input bit:
 
 <p>
-    <img  class="center" src="res/not.jpg" width="423" />
+    <img  class="center" src="res/not.jpg" style="width:50%" />
 </p>
 
 By combining the NOT and AND gates, we get the *NAND* gate:
 
 <p>
-    <img  class="center" src="res/nand.jpg" width="423" />
+    <img  class="center" src="res/nand.jpg" style="width:50%" />
 </p>
 
 And NOT and OR create *NOR*:
 
 <p>
-    <img  class="center" src="res/nor.jpg" width="423" />
+    <img  class="center" src="res/nor.jpg" style="width:50%" />
 </p>
 
 There are a few other gates, but this is enough for most things. We'll add more as the need arises!
@@ -157,12 +157,12 @@ The text of this chapter was written by [James Schloss](https://github.com/leios
 [<p><img  class="center" src="../cc/CC-BY-SA_icon.svg" /></p>](https://creativecommons.org/licenses/by-sa/4.0/)
 
 ##### Images/Graphics
-- The image "[ANDgate](res/and.jpg)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
-- The image "[ORgate](res/or.jpg)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
-- The image "[XORgate](res/xor.jpg)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
-- The image "[NOTgate](res/not.jpg)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
-- The image "[NANDgate](res/nand.jpg)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
-- The image "[NORgate](res/nor.jpg)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[ANDgate](res/and.jpg)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[ORgate](res/or.jpg)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[XORgate](res/xor.jpg)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[NOTgate](res/not.jpg)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[NANDgate](res/nand.jpg)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[NORgate](res/nor.jpg)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
 
 ##### Pull Requests
 

contents/IFS/res/IFS_square_1.png

@@ -72,7 +72,7 @@ This means that we need to go through the vector $$\mathcal{O}(n^2)$$ times with
 [import:1-11, lang:"v"](code/v/bubble_sort.v)
 {% sample lang="scratch" %}
 <p>
-  <img  class="center" src="code/scratch/bubble_sort.svg" width="400" />
+  <img  class="center" src="code/scratch/bubble_sort.svg" style="width:75%"/>
 </p>
 {% sample lang="coffee" %}
 [import:1-6, lang:"coffeescript"](code/coffeescript/bubblesort.coffee)

contents/IFS/res/IFS_square_2.png

@@ -12,7 +12,7 @@ The text of this chapter was written by [James Schloss](https://github.com/leios
 [<p><img  class="center" src="../cc/CC-BY-SA_icon.svg" /></p>](https://creativecommons.org/licenses/by-sa/4.0/)
 
 ##### Images/Graphics
-- The image "[example Image](res/example.png)" was created by [James Schloss](https://github.com/leios) and is licenced under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
+- The image "[example Image](res/example.png)" was created by [James Schloss](https://github.com/leios) and is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode).
 
 ##### Pull Requests
 

contents/IFS/res/IFS_square_vid_1.mp4

@@ -0,0 +1,60 @@
+#include <iostream>
+#include <string>
+
+std::string computus(int year, bool servois = false) {
+  // Year's position on the 19 year metonic cycle
+  int a = year % 19;
+
+  // Century index
+  int k = year / 100;
+
+  // Shift of metonic cycle, add a day offset every 300 years
+  int p = (13 + 8 * k) / 25;
+
+  // Correction for non-observed leap days
+  int q = k / 4;
+
+  // Correction to starting point of calculation each century
+  int M = (15 - p + k - q) % 30;
+
+  // Number of days from March 21st until the full moon
+  int d = (19 * a + M) % 30;
+
+  // Returning if user wants value for Servois' table
+  if (servois) {
+    return std::to_string((21 + d) % 31);
+  }
+
+  // Finding the next Sunday
+  // Century-based offset in weekly calculation
+  int N = (4 + k - q) % 7;
+
+  // Correction for leap days
+  int b = year % 4;
+  int c = year % 7;
+
+  // Days from d to next Sunday
+  int e = (2 * b + 4 * c + 6 * d + N) % 7;
+
+  // Historical corrections for April 26 and 25
+  if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {
+    e = -1;
+  }
+
+  // Determination of the correct month for Easter
+  return 22 + d + e > 31 ? "April " + std::to_string(d + e - 9)
+                         : "March " + std::to_string(22 + d + e);
+}
+
+// Here, we will output the date of the Paschal full moon (using Servois
+// notation), and Easter for 2020-2030
+int main() {
+  std::cout << "The following are the dates of the Paschal full moon (using "
+               "Servois notation) and the date of Easter for 2020-2030 AD:\n"
+               "Year\tServois number\tEaster\n";
+
+  for (int year = 2020; year <= 2030; year++) {
+    std::cout << year << "\t\t" << computus(year, true) << '\t'
+              << computus(year) << std::endl;
+  }
+}

contents/IFS/res/IFS_triangle_1.png

@@ -0,0 +1,68 @@
+#include <stdio.h>
+
+char *computus(int year, int servois, char *out, size_t out_size) {
+    // Year's position on the 19 year metonic cycle
+    int a = year % 19;
+
+    // Century index
+    int k = year / 100;
+
+    //Shift of metonic cycle, add a day offset every 300 years
+    int p = (13 + 8 * k) / 25;
+
+    // Correction for non-observed leap days
+    int q = k / 4;
+
+    // Correction to starting point of calculation each century
+    int M = (15 - p + k - q) % 30;
+
+    // Number of days from March 21st until the full moon
+    int d = (19 * a + M) % 30;
+
+    // Returning if user wants value for Servois' table
+    if (servois) {
+        snprintf(out, out_size, "%d",(21 + d) % 31);
+        return out;
+    }
+
+    // Finding the next Sunday
+    // Century-based offset in weekly calculation
+    int N = (4 + k - q) % 7;
+
+    // Correction for leap days
+    int b = year % 4;
+    int c = year % 7;
+
+    // Days from d to next Sunday
+    int e = (2 * b + 4 * c + 6 * d + N) % 7;
+
+    // Historical corrections for April 26 and 25
+    if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {
+        e = -1;
+    }
+
+    if ((22 + d + e) > 31) {
+        snprintf(out, out_size, "April %d", d + e - 9);
+    } else {
+        snprintf(out, out_size, "March %d", 22 + d + e);
+    }
+
+    return out;
+}
+
+int main() {
+    char tmp1[9], tmp2[9];
+
+    printf("The following are the dates of the Paschal full moon (using "
+           "Servois notation) and the date of Easter for 2020-2030 AD:\n");
+
+    printf("Year\tServois number\tEaster\n");
+
+    for (int year = 2020; year <= 2030; year++) {
+        printf("%d\t\t%s\t%s\n", year, computus(year, 1, tmp1, 9),
+               computus(year, 0, tmp2, 9));
+    }
+
+    return 0;
+}
+