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diff --git a/presentation/presentation.html b/presentation/presentation.html deleted file mode 100644 index 31c1443..0000000 --- a/presentation/presentation.html +++ /dev/null @@ -1,411 +0,0 @@ -<!DOCTYPE html> -<html> -<head> - <meta charset="utf-8"> - <meta name="generator" content="pandoc"> - <meta name="author" content="JP Appel"> - <meta name="author" content="David Marrero"> - <title>HPC Complex Fractal Generation</title> - <meta name="apple-mobile-web-app-capable" content="yes"> - <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent"> - <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui"> - <link rel="stylesheet" href="https://unpkg.com/reveal.js@^4//dist/reset.css"> - <link rel="stylesheet" href="https://unpkg.com/reveal.js@^4//dist/reveal.css"> - <style> - .reveal .sourceCode { /* see #7635 */ - overflow: visible; - } - code{white-space: pre-wrap;} - span.smallcaps{font-variant: small-caps;} - span.underline{text-decoration: underline;} - div.column{display: inline-block; vertical-align: top; width: 50%;} - div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} - ul.task-list{list-style: none;} - .display.math{display: block; text-align: center; margin: 0.5rem auto;} - </style> - <link rel="stylesheet" href="https://unpkg.com/reveal.js@^4//dist/theme/black.css" id="theme"> -</head> -<body> - <div class="reveal"> - <div class="slides"> - -<section id="title-slide"> - <h1 class="title">HPC Complex Fractal Generation</h1> - <p class="author">JP Appel</p> - <p class="author">David Marrero</p> -</section> - -<section> -<section id="prerequisite-knowledge" class="title-slide slide level1"> -<h1>Prerequisite Knowledge</h1> - -</section> -<section id="complex-numbers" class="slide level2"> -<h2>Complex Numbers</h2> -<p><span class="math display"><em>i</em><sup>2</sup> = − 1</span> <span -class="math display"><em>z</em> = <em>x</em> + <em>i</em><em>y</em></span></p> -<aside class="notes"> -<ul> -<li>complex numbers are an extension of real numbers, stemming from the -square root of <span class="math inline"> − 1</span></li> -<li>a complex number is just a pair of two real numbers (x,y) with -different ways to add and multiply</li> -<li>in computer science we model real numbers with a single float or -double, so we will need 2 floats or doubles to model a complex -number</li> -</ul> -</aside> -<div class="fragment"> -<h3 id="addition">Addition</h3> -<p><span -class="math display"><em>z</em><sub>1</sub> + <em>z</em><sub>2</sub> = (<em>x</em><sub>1</sub>+<em>x</em><sub>2</sub>) + <em>i</em>(<em>y</em><sub>1</sub>+<em>y</em><sub>2</sub>)</span></p> -<aside class="notes"> -<ul> -<li>addition behaves as you expect</li> -<li>multiplication involves multiplying then distributing, and using the -fact that <span -class="math inline"><em>i</em><sup>2</sup> = − 1</span></li> -<li>so adding two complex numbers is 2 float additions</li> -<li>and multiplying them is 4 multiplications and 2 additions</li> -</ul> -</aside> -<h3 id="multiplication">Multiplication</h3> -<p><span -class="math display"><em>z</em><sub>1</sub><em>z</em><sub>2</sub> = (<em>x</em><sub>1</sub><em>x</em><sub>2</sub>−<em>y</em><sub>1</sub><em>y</em><sub>2</sub>) + <em>i</em>(<em>x</em><sub>1</sub><em>y</em><sub>2</sub>+<em>x</em><sub>2</sub><em>y</em><sub>1</sub>)</span></p> -</div> -</section> -<section id="what-is-the-mandelbrot-set" class="slide level2"> -<h2>What is the Mandelbrot Set</h2> -<div class="fragment"> -<p><span -class="math display"><em>z</em><sub><em>n</em></sub> = <em>z</em><sub><em>n</em> − 1</sub><sup>2</sup> + <em>z</em><sub>0</sub></span></p> -<aside class="notes"> -<ul> -<li>this sequence is used to generate the mandelbrot set</li> -<li>if for some complex number <span -class="math inline"><em>z</em><sub>0</sub></span> the sequence remains -bounded as it <span class="math inline"><em>n</em></span> approaches -infinity then <span class="math inline"><em>z</em><sub>0</sub></span> -lies within the mandelbrot set</li> -<li>there are many recursive sequences related to this, where you modify -that happens with the recursive term</li> -</ul> -</aside> -</div> -</section> -<section id="fractals" class="slide level2"> -<h2>Fractals</h2> -<div class="columns"> -<div class="column" style="width:40%;"> -<ul> -<li>infinite self-similar geometric shape</li> -<li>have “fractional dimension”</li> -</ul> -</div><div class="column" style="width:60%;"> -<figure> -<img -data-src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/45/Sierpinski_triangle.svg/1920px-Sierpinski_triangle.svg.png" -style="width:80.0%" alt="Sripenski Triangle" /> -<figcaption aria-hidden="true">Sripenski Triangle</figcaption> -</figure> -</div> -</div> -<div class="fragment"> -<p>The Mandelbrot set is a fractal in the complex plane</p> -<aside class="notes"> -<ul> -<li>fractals are a infinite self-similar geometric shape</li> -<li>so if you zoom in on any one part it will look like the entire -object</li> -<li>the Sripenski triangle is an example of a fractal</li> -<li>the mandelbrot set forms a fractal in the complex plane</li> -</ul> -</aside> -</div> -</section> -<section id="fractal-in-nature" class="slide level2"> -<h2>Fractal in Nature</h2> -<figure> -<img -data-src="https://www.rocketgardens.co.uk/wp-content/uploads/2016/02/Cauliflower20Romanesco.jpg" -style="width:50.0%" alt="Romanesco Cauliflower" /> -<figcaption aria-hidden="true">Romanesco Cauliflower</figcaption> -</figure> -<aside class="notes"> -<ul> -<li>fractals often show up in nature</li> -</ul> -</aside> -</section> -<section id="escape-time-algorithm" class="slide level2"> -<h2>Escape Time Algorithm</h2> -<div> -<ul> -<li class="fragment">Inputs -<ul> -<li class="fragment">Maximum Number of iterations</li> -<li class="fragment">Upper bound</li> -</ul></li> -</ul> -<ol type="1"> -<li class="fragment">Create a grid of points to sample</li> -<li class="fragment">For each point in the sample space -<ol type="1"> -<li class="fragment">Compute the next term in the sequence</li> -<li class="fragment">if greater than the upper bound return the number -of iterations</li> -<li class="fragment">else repeat until the maximum number of iterations -and return</li> -</ol></li> -</ol> -</div> -<aside class="notes"> -<ul> -<li>to compute the complex sets we used an escape time algorithm</li> -<li>in general it takes in a maximum number of iterations, an initial -value, and an upper bound</li> -<li>the escape time algorithm is as follows (read of the slides)</li> -<li>note that each sampled point is completely independent of any other -point -<ul> -<li>this hints to us that the problem will parallelize well</li> -</ul></li> -<li>for most of the sets we looked at, there is a proven bound -<ul> -<li>ie if the sequence is ever larger than a value we know it -diverges</li> -</ul></li> -</ul> -</aside> -</section></section> -<section> -<section id="implementation" class="title-slide slide level1"> -<h1>Implementation</h1> - -</section> -<section id="program-structure" class="slide level2"> -<h2>Program Structure</h2> -<p><img data-src="diagram.png" /></p> -<aside class="notes"> -<ul> -<li>the translation units are roughly as pictured here</li> -<li>black ellipses are for serial code, color is for parallel</li> -<li>each version of the program fills in an array with the number of -iterations it took the sequence to grow too large</li> -<li>that array along with some extra data is a grid object, which can be -serialized and deserialized</li> -<li>the main fractals unit handles cli argument parsing for the sampling -resolution, fractal type etc</li> -<li>a separate renderer program handles creating images from the -<code>.grid</code> file</li> -<li>the <code>.grid</code> file format is really simple, it’s a magic -number, the grid dimensions, the maximum number of iterations, the lower -left and upper right most points of the region, and then the data</li> -</ul> -</aside> -</section> -<section id="mandelbrot" class="slide level2"> -<h2>Mandelbrot</h2> -<p><a href="../examples/mandelbrot.png">Image</a></p> -<aside class="notes"> -<ul> -<li>when mandelbrot initially tried to have this printed, the printers -kept removing the “dust” thinking it was an error in their printing -process</li> -</ul> -</aside> -</section> -<section id="tricorn" class="slide level2"> -<h2>Tricorn</h2> -<p><a href="../examples/tricorn.png">Image</a></p> -</section> -<section id="burning-ship" class="slide level2"> -<h2>Burning Ship</h2> -<p><a href="../examples/burning_ship.png">Image</a></p> -</section> -<section id="multibrot" class="slide level2"> -<h2>Multibrot</h2> -<p><a href="../examples/multibrot.png">Image</a></p> -</section> -<section id="multicorn" class="slide level2"> -<h2>Multicorn</h2> -<p><a href="../examples/multicorn.gif">GIF</a></p> -</section> -<section id="julia" class="slide level2"> -<h2>Julia</h2> -<p><a href="../examples/julia.png">Image</a></p> -</section></section> -<section> -<section id="analysis" class="title-slide slide level1"> -<h1>Analysis</h1> - -</section> -<section id="section" class="slide level2"> -<h2></h2> -<p><a href="../analysis/analysis.html">Interactive Plots</a></p> -</section></section> - </div> - </div> - - <script src="https://unpkg.com/reveal.js@^4//dist/reveal.js"></script> - - <!-- reveal.js plugins --> - <script src="https://unpkg.com/reveal.js@^4//plugin/notes/notes.js"></script> - <script src="https://unpkg.com/reveal.js@^4//plugin/search/search.js"></script> - <script src="https://unpkg.com/reveal.js@^4//plugin/zoom/zoom.js"></script> - - <script> - - // Full list of configuration options available at: - // https://revealjs.com/config/ - Reveal.initialize({ - // Display controls in the bottom right corner - controls: true, - - // Help the user learn the controls by providing hints, for example by - // bouncing the down arrow when they first 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