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Dimitri Lozeve 2020-08-27 15:01:49 +02:00
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<section>
<h2>Table of Contents</h2><ul>
<li><a href="#the-apl-family-of-languages">The APL family of languages</a><ul>
<div id="toc"><h2>Table of Contents</h2><ul>
<li><a href="#the-apl-family-of-languages">The APL family of languages</a>
<ul>
<li><a href="#why-apl">Why APL?</a></li>
<li><a href="#implementations">Implementations</a></li>
</ul></li>
<li><a href="#the-ising-model-in-apl">The Ising model in APL</a></li>
<li><a href="#conclusion">Conclusion</a></li>
</ul>
</ul></div>
<h2 id="the-apl-family-of-languages">The APL family of languages</h2>
<h3 id="why-apl">Why APL?</h3>
<p>I recently got interested in <a href="https://en.wikipedia.org/wiki/APL_(programming_language)">APL</a>, an <em>array-based</em> programming language. In APL (and derivatives), we try to reason about programs as series of transformations of multi-dimensional arrays. This is exactly the kind of style I like in Haskell and other functional languages, where I also try to use higher-order functions (map, fold, etc) on lists or arrays. A developer only needs to understand these abstractions once, instead of deconstructing each loop or each recursive function encountered in a program.</p>
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</code></pre>
<ul>
<li>We draw a random lattice of size ⍺ with <code>L ⍺</code>.</li>
<li>We apply to it our update function, with $<em>β</em>$=10, ⍵ times (using the <code>⍣</code> function, which applies a function <span class="math inline">\(n\)</span> times.</li>
<li>We apply to it our update function, with $β$=10, ⍵ times (using the <code>⍣</code> function, which applies a function <span class="math inline">\(n\)</span> times.</li>
<li>Finally, we display -1 as a space and 1 as a domino ⌹.</li>
</ul>
<p>Final output, with a <span class="math inline">\(80\times 80\)</span> random lattice, after 50000 update steps:</p>