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aria-label="search" autocomplete="off" placeholder="Search..." > </search> <button type="button" class="btn btn-link text-decoration-none" id="search-cancel">Cancel</button></div></header><div class="row flex-grow-1"><main aria-label="Main Content" class="col-12 col-lg-11 col-xl-9 px-md-4"><div id="post-list" class="flex-grow-1 px-xl-1"><article class="card-wrapper card"> <a href="/posts/split-ring-computation/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">Split Computation on Rings</h1><div class="card-text content mt-0 mb-3"><p>Idea If two numbers mod 15 can be summed mod 15 and those two numbers can be summed mod 3 and mod 5, can you the ‘sum’ computation be split?… For example, if we want to compute $ 9 + 13 \pmod{15}...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1790751600" data-df="ll" > 2026-09-30 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, CS </span></div></div></div></div></a></article><article class="card-wrapper card"> <a href="/posts/i-love-my-bf-bsides-ctf/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">I love my BF Challenges at BSidesSF 2026</h1><div class="card-text content mt-0 mb-3"><p>My friend, iagox86, invited me to write a few challenges for the BSidesSF 2026 CTF so I wrote a few challenges around BrainFuck (BF). Here’s how they work and how to solve them. Context If you’re...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1774162800" data-df="ll" > 2026-03-22 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, CS </span></div></div></div></div></a></article><article class="card-wrapper card"> <a href="/posts/bf-instruction-finder/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">BrainFuck Instruction Finder</h1><div class="card-text content mt-0 mb-3"><p>Searching through trillions of code snippets in minutes This is a post about… writing code to generate BF code that can do any computation. If you’re not familiar with BF, this post will explain e...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1739174400" data-df="ll" > 2025-02-10 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, CS </span></div></div></div></div></a></article><article class="card-wrapper card"> <a href="/posts/string-art-portraits/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">String Art Portraits</h1><div class="card-text content mt-0 mb-3"><p>This post is a high-level overview of how I wrote code generate instructions that turns an image into instructions to make string art portraits: Many others have done this and taken it well be...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1676793600" data-df="ll" > 2023-02-19 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, CS </span></div></div></div></div></a></article><article class="card-wrapper card"> <a href="/posts/middle-order-vs-merge-sort/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">Merge Order vs Merge Sort</h1><div class="card-text content mt-0 mb-3"><p>Efficiently Joining Data, Maybe… This post is about replacing the traditional Merge Sort merge step when joining/merging large datasets with a sort of “Merge Order” merge and attempt to calculate ...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1671696000" data-df="ll" > 2022-12-22 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, CS </span></div></div></div></div></a></article><article class="card-wrapper card"> <a href="/posts/middle-order/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">Middle Order</h1><div class="card-text content mt-0 mb-3"><p>This post is about solving a very particular and unimportant problem: Given a number, N, efficiently generate the sequence of all the numbers in [0, N) in a “middle order” where each number appears...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1668326400" data-df="ll" > 2022-11-13 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, CS </span></div></div></div></div></a></article><article class="card-wrapper card"> <a href="/posts/arena-lineups-and-state-transitions/" class="post-preview row g-0 flex-md-row-reverse"><div class="col-md-12"><div class="card-body d-flex flex-column"><h1 class="card-title my-2 mt-md-0">Arena Lineups and State Transitions</h1><div class="card-text content mt-0 mb-3"><p>In a video game I’ve played a lot recently there are online arenas where players line up, the two people at the front of the line fight, then the loser goes to the back of the line. Even with a rel...</p></div><div class="post-meta flex-grow-1 d-flex align-items-end"><div class="me-auto"> <i class="far fa-calendar fa-fw me-1"></i> <time data-ts="1589094000" data-df="ll" > 2020-05-10 </time> <i class="far fa-folder-open fa-fw me-1"></i> <span class="categories"> Math, All </span></div></div></div></div></a></article></div></main><aside aria-label="Panel" id="panel-wrapper" class="col-xl-3 ps-2 text-muted"><div class="access"><section id="access-lastmod"><h2 class="panel-heading">Recently Updated</h2><ul class="content list-unstyled ps-0 pb-1 ms-1 mt-2"><li class="text-truncate lh-lg"> <a href="/posts/split-ring-computation/">Split Computation on Rings</a><li class="text-truncate lh-lg"> <a href="/posts/i-love-my-bf-bsides-ctf/">I love my BF Challenges at BSidesSF 2026</a><li class="text-truncate lh-lg"> <a href="/posts/bf-instruction-finder/">BrainFuck Instruction Finder</a><li class="text-truncate lh-lg"> <a href="/posts/string-art-portraits/">String Art Portraits</a><li class="text-truncate lh-lg"> <a href="/posts/middle-order-vs-merge-sort/">Merge Order vs Merge Sort</a></ul></section><section><h2 class="panel-heading">Trending Tags</h2><div class="d-flex flex-wrap mt-3 mb-1 me-3"> <a class="post-tag btn btn-outline-primary" href="/tags/computer-science/">computer-science</a> <a class="post-tag btn btn-outline-primary" href="/tags/bf/">bf</a> <a class="post-tag btn btn-outline-primary" href="/tags/math/">math</a> <a class="post-tag btn btn-outline-primary" href="/tags/art/">art</a> <a class="post-tag btn btn-outline-primary" href="/tags/compilers/">compilers</a> <a class="post-tag btn btn-outline-primary" href="/tags/ctf/">ctf</a> <a class="post-tag btn btn-outline-primary" href="/tags/videogames/">videogames</a></div></section></div></aside></div><div class="row"><div id="tail-wrapper" class="col-12 col-lg-11 col-xl-9 px-md-4"><footer aria-label="Site Info" class=" d-flex flex-column justify-content-center text-muted flex-lg-row justify-content-lg-between align-items-lg-center pb-lg-3 " ><p>© <time>2026</time> <a href="https://github.com/mikelmcdaniel">Mikel Mcdaniel</a>. <span data-bs-toggle="tooltip" data-bs-placement="top" title="Except where otherwise noted, the blog posts on this site are licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) License by the author." >Some rights reserved.</span></p><p>Using the <a data-bs-toggle="tooltip" data-bs-placement="top" title="v7.5.0" href="https://github.com/cotes2020/jekyll-theme-chirpy" target="_blank" rel="noopener" >Chirpy</a> theme for <a href="https://jekyllrb.com" target="_blank" rel="noopener">Jekyll</a>.</p></footer></div></div><div id="search-result-wrapper" class="d-flex justify-content-center d-none"><div class="col-11 content"><div id="search-hints"><section><h2 class="panel-heading">Trending Tags</h2><div class="d-flex flex-wrap mt-3 mb-1 me-3"> <a class="post-tag btn btn-outline-primary" href="/tags/computer-science/">computer-science</a> <a class="post-tag btn btn-outline-primary" href="/tags/bf/">bf</a> <a class="post-tag btn btn-outline-primary" href="/tags/math/">math</a> <a class="post-tag btn btn-outline-primary" href="/tags/art/">art</a> <a class="post-tag btn btn-outline-primary" href="/tags/compilers/">compilers</a> <a class="post-tag btn btn-outline-primary" href="/tags/ctf/">ctf</a> <a class="post-tag btn btn-outline-primary" href="/tags/videogames/">videogames</a></div></section></div><div id="search-results" class="d-flex flex-wrap justify-content-center text-muted mt-3"></div></div></div></div><aside aria-label="Scroll to Top"> <button id="back-to-top" type="button" class="btn btn-lg btn-box-shadow"> <i class="fas fa-angle-up"></i> </button></aside></div><div id="mask" class="d-none position-fixed w-100 h-100 z-1"></div><aside id="notification" class="toast" role="alert" aria-live="assertive" aria-atomic="true" data-bs-animation="true" data-bs-autohide="false" ><div class="toast-header"> <button type="button" class="btn-close ms-auto" data-bs-dismiss="toast" aria-label="Close" ></button></div><div class="toast-body text-center pt-0"><p class="px-2 mb-3">A new version of content is available.</p><button type="button" class="btn btn-primary" aria-label="Update"> Update </button></div></aside><script> document.addEventListener('DOMContentLoaded', () => { SimpleJekyllSearch({ searchInput: document.getElementById('search-input'), resultsContainer: document.getElementById('search-results'), json: '/assets/js/data/search.json', searchResultTemplate: '<article class="px-1 px-sm-2 px-lg-4 px-xl-0"><header><h2><a href="{url}">{title}</a></h2><div class="post-meta d-flex flex-column flex-sm-row text-muted mt-1 mb-1"> {categories} {tags}</div></header><p>{content}</p></article>', noResultsText: '<p class="mt-5">Oops! 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