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jdreplicator.html
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<!DOCTYPE html>
<html lang="en-US">
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last modified 18.11.2022
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<title>Dietz replicator</title>
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<div class="header">
<span3>Cite as: </span3><div>Dietz Replicator <a href="http:https://imar.ro/~mbuliga/index.html">© Marius Buliga</a> (2022), https://mbuliga.github.io/quinegraphs/jdreplicator.html<span id="citeas"></span></div>
<span3>See also:</span3><br> <a href="https://chemlambda.github.io/index.html">All chemlambda projects</a><br><br>
<br><br>
The Dietz replicator (aka JD replicator) was found after random searches in the <a href="https://mbuliga.github.io/quinegraphs/quinelab.html#random_10_quine_bubbles">9 billion family of graphs which you can also explore</a>. <br><br>
It is a chemlambda molecule with the property that it produces a finite, but random length string of application A and fanout FOE nodes. <br><br>
It looks like this:
<div class="row">
<div class="col-6 menu" style="text-align: center;">
<img src="img/jdc/jdreplicator-1.jpg" alt="Dietz replicator" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><br><br>
</div></div><br><br>
It has <a href="https://arxiv.org/abs/2003.14332">the code</a>:<br><br> <span3>L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in</span3><br><br>
If we let it reduce randomly, it can take random shapes, like this: <br><br>
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<img src="img/jdc/jdreplicator-2.jpg" alt="Dietz replicator random 1" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><img src="img/jdc/jdreplicator-3.jpg" alt="Dietz replicator random 2" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><img src="img/jdc/jdreplicator-4.jpg" alt="Dietz replicator random 3" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><br><br>
</div></div><br><br>
It can be used with any <a href="https://mbuliga.github.io/quinegraphs/lambda2mol.html#lambdanote">molecule obtained from a lambda term</a>. Mind that the Dietz replicator does not represent a lambda term! <br><br>
It will produce a finite but random number of pairs of the initial template, even if the template molecule itself reduces in the same time. <br><br>
Indeed, let's glue the Dietz replicator to the 1-node molecule which represents the identity lambda term. The molecule obtained has <a href="https://arxiv.org/abs/2003.14332">the code</a>:<br><br>
<span3>L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in</span3>^L a7 a7 a1<br><br>
and it looks like this:<br><br>
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<img src="img/jdc/jdreplicator-id-1.jpg" alt="Dietz replicator with Id" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><br><br>
</div></div><br><br>
If we let it reduce randomly, it produces a random number of pairs of Id molecules, like this: <br><br>
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<img src="img/jdc/jdreplicator-id-2.jpg" alt="Dietz replicator with Id random 1" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><img src="img/jdc/jdreplicator-id-3.jpg" alt="Dietz replicator with Id random 2" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><img src="img/jdc/jdreplicator-id-4.jpg" alt="Dietz replicator with Id random 3" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><br><br>
</div></div><br><br>
The same can be tried with the <a href="https://mbuliga.github.io/quinegraphs/lambda2mol.html#omega">Omega combinator molecule</a>. The molecule obtained has <a href="https://arxiv.org/abs/2003.14332">the code</a>:<br><br>
<span3>L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in</span3>^L a2 a3 a4^FO a3 a5 a6^A a5 a6 a2^A a4 a7 a1^L a8 a9 a7^FO a9 a10 a11^A a10 a11 a8<br><br>
and it looks like this:<br><br>
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<img src="img/jdc/jdreplicator-omega-1.jpg" alt="Dietz replicator with Omega" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><br><br>
</div></div><br><br>
Differently from the Id molecule, the Omega molecule is a <a href="https://mbuliga.github.io/quinegraphs/ic-vs-chem.html#icvschem">chemlambda quine</a>. That means it reduces forever, it does not have a final shape.<br><br>
If we let the Dietz replicator + Omega to reduce randomly, it produces a random number of pairs of Omega molecules, which are all in various stages of reduction themselves, and they will continue to reduce forever! Snapshots look like like this: <br><br>
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<img src="img/jdc/jdreplicator-omega-2.jpg" alt="Dietz replicator with Omega random 1" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><img src="img/jdc/jdreplicator-omega-3.jpg" alt="Dietz replicator with Omega random 2" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><img src="img/jdc/jdreplicator-omega-4.jpg" alt="Dietz replicator with Omega random 3" style="padding: 20px; margin-bottom: 18px; width:350px;border:0"><br><br>
</div></div><br><br>
The ability of this replicator is that it produces copies of active molecules, while they continue to function. This is a far harder to achieve property than just replication. But Nature can do this, for sure: living cells reproduce while they also continue to have a metabolism. In Nature there is no clear separation between functioning (metabolism) and pure replication. <br><br>
You can run the simulations by yourself, just use the lower part of this page. <br><br> <br><br>
This page is a response to the kind request of Joel Dietz, the creator of <a href="http:https://metalambda.org/">metalambda.org</a>, for his <a href="http:https://metaseminar.io">metaseminar 0</a> (link to be updated if transcript available).
<br><br>
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</div>
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<div class="col-1 menu" style="text-align: left;"><div class="scol-12"> <span3 id="agetext">random choices </span3><br><br> <span3 id="buttonAge" class="image2" ></span3></div>
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<ul>
<li>
<span2>
<select class="theme-construction" id="listofmols" onchange="selectionStarter();">
<option value="howtolab">MENU</option>
<option value="jdreplicator">"Dietz replicator"</option>
<option value="jdreplicatorId">"Dietz replicator with Identity"</option>
<option value="jdreplicatorOmega">"Dietz replicator with Omega"</option>
</select>
</span2>
</li>
<li></li>
<li> <span3 id="buttonImportMol" class="image2" ></span3> <span3 id="buttonUpdateMol" class="image2" ></span3>
</li>
<li> <span3>for edges use only 0-9,a-z,A-Z</span3>
</li>
<li><div><textarea id="inputmol" class="image2" style="height: 80px; width: 80%; background-color: #010101;
color: #6495ED; font-size: 14px;">L 0 8 12^FI 1 2 0^A 3 4 14^FI 5 6 10^FOE 8 2 6^FOE 9 5 4^A 10 in 1^FOE 12 13 3^A 13 14 9^Arrow a1 in</textarea> </div>
</li>
<li>
<span3>rewrites weights slider</span3> <div class="slidecontainer">GROW <input class="slider" type="range" min="0" max="100" value="50" id="rewritesRange"> SLIM</div>
</li>
</ul>
</div>
<div class="col-4 menu" style="text-align: left;">
<span3 style="text-align: left;"> nodes ∼ </span3><span id="nodenumber"></span>
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<div class="scol-12"> <span3 id="button0" class="image2" ></span3></div>
<div class="scol-12"> <span3 id="button1" class="image2" ></span3></div>
<div class="scol-12"> <span3 id="button2" class="image2" ></span3></div>
<div class="scol-12"> <span3 id="button3" class="image2" ></span3></div>
<div class="scol-12"> <span3 id="button4" class="image2" ></span3></div>
</div>
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<ul>
<li> <div id="svgdiv"> </div></li>
<li><span3>gravity slider</span3> <div class="slidecontainer">MIN <input class="slider" type="range" min="1" max="250" value="150" id="gravRange"> MAX</div></li>
<li><span2>CODE: </span2><span id="molyoulookat"></span></li>
<li><span> (Rewrites stop at max. </span><span id="maxnodenumber">512</span> nodes<span>)</span></li>
</ul>
</div>
<div class="col-4 menu" style="text-align: left;">
<span id="comments" ></span><br><br>
<span3 style="text-align: left;" id="errors"></span3>
</div>
</div>
<div class="row">
<div class="scol-6" style="text-align: left;">
<span2>before:</span2><br><br>
<span id="puttransformcachealt"></span>
</div>
<div class="scol-6" style="text-align: left;">
<span2>chosen:</span2><br><br>
<span id="chosentransform"></span>
</div>
<div class="scol-6" style="text-align: left;">
<span2>after:</span2><br><br>
<span id="puttransformcachealtafter"></span>
</div>
<div class="scol-6" style="text-align: left;">
<span2>mol before:</span2><br><br>
<span id="molexport"></span>
</div>
<div class="scol-6" style="text-align: left;">
<span2>mol after:</span2><br><br>
<span id="molexportafter"></span>
</div>
</div>
<script src="js/iceMol.js"></script>
<script src="js/iceComments.js"></script>
<script src="js/parameters.js"></script>
<script src="js/nodes.js"></script>
<script src="js/chemistry.js"></script>
<!-- <script src="js/reactions.js"></script> -->
<script src="js/myD3Graph.js"></script>
<script src="js/icequine.js"></script>
<script>
var whichP = location.hash;
whichP = whichP.replace(/#/g, "");
if (whichP != "") {
document.getElementById("listofmols").value = whichP;
}
whichButtons(whichP);
selectionStarter();
</script>
</body>
</html>