Answers.Body: <p><strong>Systems Approach</strong></p>
  
  <p>Let's set out to replicate a real time system <span class="math-container">$S: \mathcal{X} \Rightarrow \mathcal{Y} \; | \; I$</span>, where <span class="math-container">$\mathcal{X}$</span> is a empirical continuous history of input and <span class="math-container">$\mathcal{Y}$</span> empirical continuous history of output, conditioned upon a real initial system state <span class="math-container">$I$</span>.  Based on some definition, we require <span class="math-container">$S$</span> to be alive.</p>
  
  <p>We cannot simulate a replication of a theoretical model of life, with a selfish gene or any other such attribute, simply because no mathematically terse model on which the simulation could be based exists.  As of this writing, only hints to and minutia of such a model are known.</p>
  
  <p>Furthermore, models are mathematical representations that, throughout human history, are found to be approximations of complexities once anomalies are addressed and new models develop to incorporate them into the theory.<sup>1</sup></p>
  
  <p><strong>Simulation Roughly Defined</strong></p>
  
  <p>If we examine a general algorithm <span class="math-container">$\mathcal{A}$</span> to replicate <span class="math-container">$S$</span>, replication can be roughly sketched as follows.</p>
  
  <ul>
  <li>Estimate system <span class="math-container">$S$</span>, essentially forming hypothesis <span class="math-container">$H$</span>.</li>
  <li>Simulate initial state <span class="math-container">$I$</span>.</li>
  <li>Initiate a series of discrete stimuli <span class="math-container">$\mathcal{X}_t$</span> approximating the real and continuous <span class="math-container">$\mathcal{X}$</span>.</li>
  <li>Acquire resulting system behavior <span class="math-container">$\mathcal{Y}_t$</span> as discrete observations of <span class="math-container">$\mathcal{Y}$</span>.</li>
  <li>Verify the difference between simulated and actual systems to be within allowable error <span class="math-container">$\epsilon$</span>. </li>
  </ul>
  
  <p><strong>Defining Spontaneous Emergence</strong></p>
  
  <p>By spontaneous emergence is meant that such an astronomically large array of initial states and sequences of stimuli occurred that there is a high probability of one of the permutations being alive, based on some specific and reasonable definition of what is living.</p>
  
  <p><strong>Defining What Life Is</strong></p>
  
  <p>Reviewing several definitions of living organisms, the most reasonable definitions include these:</p>
  
  <ul>
  <li>The organism can be distinguished from its environment.</li>
  <li>The organism can acquire and cache potential energy and materials required to operate.</li>
  <li>Its operation includes continued acquisition, producing a bidirectional and sustainable relationship with its environment.</li>
  <li>The organism can roughly reproduce itself.</li>
  <li>The reproduction is similar to but not exactly like the parent(s).</li>
  <li>The method of energy and materials acquisition may include the consumption of other organisms or its energy and materials.</li>
  </ul>
  
  <p>Competing for resources, natural selection, and all the other features of evolutionary theory are corollary to the above five requirements.  In addition to these, the current trend toward recognizing symbiogenesis as a common theme in the emergence of species should not be dismissed.</p>
  
  <ul>
  <li>Replication of one organism may be influenced by the composition of another organism through forms of assimilation or symbiosis such that traits are passed across categories of organisms.</li>
  </ul>
  
  <p><strong>Artificial Life as a Simulation</strong></p>
  
  <p>These seven criteria poses a challenge for humans attempting to artificially generate life.  It is easy to create a computer model such that life is simulated in some way.  Consider how.</p>
  
  <ul>
  <li>The environment contains virtual energy and virtual matter.</li>
  <li>The model of the organism, distinguished from its environment, can acquire its operational requirements from the environment through a set of operations on it.</li>
  <li>Mater and energy are conserved because the temperatures are far below nuclear thresholds.</li>
  <li>The model of the organism allows acquisition only if enough of the energy and materials acquisition has occurred to maintain the cache.</li>
  <li>Mater and energy acquired by one organism cannot be acquired by another organism except by consumption or absorption of an organism that acquired it or produced it from that which was acquired.</li>
  <li>The model of the organism can self-replicate in such a way that stochastic differences in the replication is introduced in small quantities.</li>
  <li>Operational information, including replication information, may be acquired through consumption or symbiotic relationship under some conditions.</li>
  </ul>
  
  <p><strong>Magical Genes for Spontaneous Life</strong></p>
  
  <p>Notice that the selfish gene is not mentioned above.  Selfishness, the prerequisite of which is intention, is not a requirement for life.  An amoeba does not think selfishly when it moves or eats.  It operates witlessly.  We should not anthropomorphize every organism we study, or develop theory based on anthropomorphic conceptions.</p>
  
  <p>Similarly, symbiotic relationships form that are neither loving nor altruistic.  They exist because there is a mutual benefit that appeared as an unintended byproduct of normal operations and both symbiotic parents happened to pass that symbiotic connection to their respective offspring. 
  The mutual benefit, the symbiosis, and the replication are witless and unintended.</p>
  
  <p>There need not be a control mechanism distinct from all other replicated mechanisms to control either symbiotic collaboration or competition.  They too are natural consequences of living things sharing an environment.  Whether an organism dies because it</p>
  
  <ul>
  <li>Lost its symbiont,</li>
  <li>Starves because other organisms consumed its necessities,</li>
  <li>The organism itself depleted its own resources, or</li>
  <li>Those needed resources were otherwise rendered unavailable,</li>
  </ul>
  
  <p>it is still unable to replicate, so its traits die with it.</p>
  
  <p>Note also that there is no known molecule that can replicate itself.  Complex systems of molecules in a variety of chemical states and equilibria are required for reproduction to take place.</p>
  
  <p><strong>Returning to Simulating an Already Existing Organism</strong></p>
  
  <p>Running a time sharing system or distributing these simulated organisms in a parallel processing arrangement may some day simulate a biosphere, but it is not one in that only transistor electro-chemistry is involved.  There is no actual direct relationship between the energy and mater of the system used to assemble the simulation and the energy and mater of the simulated environment in which the simulated systems <span class="math-container">$S$</span> reside.</p>
  
  <p>Certainly genetic algorithms, such as Avida and Tierra, have been developed.  Compare those simulations to the modelling scenario described above, and their deficiencies become clear.  Human researchers have not yet found <span class="math-container">$\mathcal{A}$</span> to replicate <span class="math-container">$S$</span> in a way that aligns with biological reality.</p>
  
  <p><strong>Open-endedness Requires Verification to Have Merit</strong></p>
  
  <p>The most significant limitation on implementations <em>in silico</em>, is that they can never be truly open-ended.</p>
  
  <p>There is no way as of this writing to replicate that which was simulated outside the simulation system.  Until nanotechnology reaches a point where 3D construction and assembly can migrate alive simulations into the unsimulated universe, these simulations are closed-ended in that way and their viability <em>in vito</em> is untested.  The value of open-ended simulations without any way to validate them is essentially zero except for amusement.</p>
  
  <p>Even in the space of digital simulation, as far as that technology has progressed, nothing even close to von Neumann's universal constructor has been accomplished.  Although generic functional copy constructors are available in Scheme, LISP, C++, Java, and later languages, such is a minuscule step toward living objects in computers.</p>
  
  <p><strong>Digital Soup</strong></p>
  
  <p>The simulation of life's origins is considerably more difficult than finding an algorithm <span class="math-container">$\mathcal{A}$</span> to replicate <span class="math-container">$S$</span>, where <span class="math-container">$S$</span> is a single life form and a sufficient portion of its environment to be representative of the biosphere on earth with an organism in it.</p>
  
  <p>The issue with primordial digital soup is one of the combinatory explosion.  There are 510 million square Km on the earth's surface, and there are only three categories of life origin time frames possible.</p>
  
  <ul>
  <li>The current estimates are close to correct, that the earth formed 4.54 billion years ago and extremely primitive life emerged 3.5 billion years ago</li>
  <li>The organic material found in Canada that is allegedly 3.95 billion years old shortens the gap between planetary formation and life formation on it and older terrestrial life may be found</li>
  <li>Vladimir Vernadsky's comment that life may have preexisted earth is more than just a possibility</li>
  </ul>
  
  <p>If we go with the 1.04 billion year gap, then <span class="math-container">$(4.54 - 3.5) \cdot 10^9 \cdot 510 \cdot 10^6$</span> Km-years of soup must be simulated, since we cannot assume that life started in the ocean or a puddle or even on the surface.  It could have started underground or in the atmosphere.  The biosphere is currently thought to be 1,800 m above to 8,372 m below thick.</p>
  
  <p>With nanobes being 20 nm in diameter and the possibility that the emergence may have only taken one second we have to simulate in three dimensions over time the following space-time domain in finite elements with at least 50% overlap in all three dimensions.</p>
  
  <p><span class="math-container">$$\dfrac {2^3 \cdot (4.54 - 3.5) \cdot 10^9 \cdot 510 \cdot 10^6 \cdot (1,800 - 8,372) \cdot 365.25 \cdot 24 \cdot 60 \cdot 60} {(20 \cdot 10^{-9})^3} \\ = 170,260,472,379 \cdot 10^{9+6+27} = 1.7 \cdot 10^{56}$$</span></p>
  
  <p>With a quantum computer two stories high the size of Switzerland, the computing time would vastly exceed the duration of the average species on earth.  Humans are likely to be extinct before the computation completes.</p>
  
  <p>As the dating of the oldest found fossils converges on the dating of earth, it may seem that life emerged quickly on earth, but that is not a logical conclusion.  If life formed as soon as the earth cooled sufficiently and no evidence of continuous emergence is found in the remaining billions of years, then Vernadsky's inference that life arrived on earth through one or more of the bodies that struck it becomes more probable.</p>
  
  <p>If that is the case, then one must ask the question, if all assumptions are dropped, whether life had a beginning at all.</p>
  
  <p><strong>Simulating Life Versus Simulating Its Formation</strong></p>
  
  <p>We may simulate what life is, that is, find an algorithm <span class="math-container">$\mathcal{A}$</span> to replicate <span class="math-container">$S$</span>, where <span class="math-container">$S$</span> is a single live organism.  It is not realistic to, by brute force, simulate how life began without learning more about what conditions can lead to its formation theoretically to drastically reduce the soup simulation space.  It is that learning that is an ongoing area of research in the genetic algorithm field.</p>
  
  <p>Early musings about the possibility of an algorithm <span class="math-container">$\mathcal{B}$</span>, which can provide the conditions that allow an arbitrary organism <span class="math-container">$S$</span> conforming to the above definition of life to form with out a parent or parents were interesting. Given algorithm <span class="math-container">$\mathcal{A}$</span> that simulates a life form and algorithm <span class="math-container">$\mathcal{B}$</span> that simulate the formation of life, it may be the later algorithm that proves significantly more difficult.</p>
  
  <p>Conforming physics outside a computer to the simulation may be impossible.  Whether simulated life, when embodied in a robotic system is actually going to be considered life will be left to our descendants, should the species endure sufficiently.</p>
  
  <p><strong>Footnotes</strong></p>
  
  <p>[1] Classic cases include the heliocentric Copernican system giving way to the Law of Gravity, that law being shown an approximation of general relativity as shown by the proper prediction of the orbit of Mercury and light's curvature near the sun, the Four Elements dismissed in light of Lavoisier's discovery of oxygen, and absolute provability of truth within a closed symbolic system disproved by Gödel in his second incompleteness theorem and then recouped partially (in terms of computability) by Turing's completeness theorem.</p>
  
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Answers.UserDisplayName: Douglas Daseeco
Answers.Body: <p>Although difficult to prove a negative, I don't think that this has been done. </p>
  
  <p>The most advanced simulations of low-level features are not capable of scaling to simulate large enough populations at large enough time scales where scientific consensus claims that this has happened in reality. </p>
  
  <p>Although you say that you are not directly interested in chemistry, but some abstract substrate, I am using chemistry as an example of the challenge. That is because creating a simplified substrate with enough rich emergent behaviour is non-trivial. The chemical elements essentially have rules about how they combine into larger physical structures (via different bonding mechanisms) and only roughly a dozen types of atom are involved. It's actually reasonably simple and tractable at the lowest level. The problems come from the multiple scales of structure - building "unit" molecules (DNA/RNA bases, protein peptides, lipids, sugar bases etc), creating polymers from those units, interactions between polymers, physical structures built and torn down by those interactions, each of which exhibits more complex behaviour. This structural hierarchy is likely required for any self-replicating machinery that is not simply being fed the higher-level units directly. In your question you want to find self-replication that is emergent, not designed . . . so feeding in these higher-level units would probably count as cheating.</p>
  
  <p>We probably don't have the computational power to properly simulate even the <a href="https://en.wikipedia.org/wiki/Miller%E2%80%93Urey_experiment" rel="nofollow noreferrer">Miller-Urey experiment</a> which is far from self-replication - chemical simulations <em>in silico</em> are limited to things like protein folding calculations, and these are far from real-time. Inside just a single bacterial cell getting ready to divide, proteins are produced and fold by the hundreds every second.</p>
  
  <p>One thing that has been done is to create a self-replicating machine in <a href="https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Self-replication" rel="nofollow noreferrer">Conway's Game of Life called "Gemini"</a>. This was designed, not spontaneously created. However, it would have a very low but non-zero chance of spontaneously being created with random initialisation. It would be a very fragile replicator though, any mutation or collision with other active elements would likely break it. The experiment of attempting to randomly/spontaneously create Gemini is not computationally feasible.</p>
  
  <p>It is likely that any physical system simple enough to be considered "primordial soup" yet rich enough to express replicating units is going to require a few layers of construction before you get to see those units. These layers need to be built up combinatorially, and odds of this happening spontaneously in a small experiment with limited computation appear to be low. You need to bear in mind the <em>extremely large</em> computation that would effectively have been done by an order of <span class="math-container">$10^{30}$</span> molecules that can interact at very fast rates in parallel (compared to rate at which these same interactions can be simulated in current CPUs), with processing times of the order <span class="math-container">$10^8$</span> years. It is mainly conjecture that this is enough to create an Initial Darwinian Ancestor - it is basically a logical extrapolation to the theory of evolution, following the Occam's Razor principle of looking for simplest compatible explanation.</p>
  
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Answers.UserDisplayName: Neil Slater
Answers.Body: <p>It's yes in cellular automata space, you have this old one from 1997:</p>
  <p><em>&quot;Emergence of self-replicating structures in a cellular automata space&quot;</em>
  <a href="http://fab.cba.mit.edu/classes/S62.12/docs/Chou_CA.pdf" rel="nofollow noreferrer">http://fab.cba.mit.edu/classes/S62.12/docs/Chou_CA.pdf</a></p>
  <p>I quote you the part of the abstract you'll be interested in:</p>
  <p><em>&quot;This article demonstrates for the first time that it is possible to create cellular automata models in which a self-replicating structure emerges from an initial state having a random density and distribution of individual components.&quot;</em></p>
  <p>And those replicators carry some kind of information and are in some minimalistic sense evolvable (the loops can grow).
  But, you'll see the emergence is mainly due to the fact that the cellular automata universe designed allow small replicators, and by just being chaotic enough those replicators form by luck. It's an Langton loop system, you have a live demo there (but quite old as well):
  <a href="https://www.complexcomputation.org/hhchou/research/research_ca_demo1.html" rel="nofollow noreferrer">https://www.complexcomputation.org/hhchou/research/research_ca_demo1.html</a></p>
  <p>I dont know any other work that come close to that in term of simulating emergence of replicators, it's old and with limitations but at least it's something.</p>
  <p>Regards.</p>
  
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Answers.UserDisplayName: Thomas Cabaret
Answers.Body: <p>Primordial replicators can be simpler than you think. Check out this video:</p>
  
  <p><a href="https://www.youtube.com/watch?v=w2lqZL153JE" rel="nofollow noreferrer">Self Replication: How molecules can make copies of themselves</a> 
  <br><sub>[Source: University of Groeningen]</sub></p>
  
  <p>In a noisy environment you get natural mutation. And voila, replication + mutation = evolution.</p>
  
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Answers.Text: It's a good link, and relevant to the conversation. However, link-only answers are not considered high quality here. It would be helpful to summarise the video in more detail, and also relate it back to the original question - which is about having this kind of organisation occur spontaneously in a silicon/code environment (whilst the video is a thought experiment which seems feasible for a chemical system).
Answers.UserDisplayName: Neil Slater
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Answers.Text: I actually don't think a summary would help; some things are better shown than explained.  But please feel free to add an answer if you like.  Also, it should be easy to imagine the solution in silico.  Actual implementation details wouldn't add much.
Answers.UserDisplayName: Ray
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Answers.Text: I have already added an answer. If a summary would not help, then please find some other way to make this answer self-contained. It is a goal of the site that question and answer pairs should not *rely* on links. A good way to assess this: If your link stopped working, would the answer still be complete and useful?
Answers.UserDisplayName: Neil Slater
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Answers.UserDisplayName: Ray
Body: <p>One of the cornerstones of The Selfish Gene (Dawkins) is the spontaneous emergence of replicators, i.e. molecules capable of replicating themselves.</p>
  <p>Has this been modeled <em>in silico</em> in open-ended evolutionary/artificial life simulations?</p>
  <p>Systems like Avida or Tierra explicitly <strong>specify</strong> the replication mechanisms; other genetic algorithm/genetic programming systems explicitly <strong>search for</strong> the replication mechanisms (e.g. to simplify the von Neumann universal constructor)</p>
  <p>Links to simulations where replicators emerge from a primordial digital soup are welcome.</p>
  
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Comments.Text: @sihubumi I'd love to see examples of such simulations too. Were you able to find anything?
Comments.UserDisplayName: Wiktor Tomczak
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Comments.Text: How "soupy" does the primordial soup need to be here? There are no simulators working at level of atomic/chemical interaction. But if we started with higher level building blocks, they are likely to include some rules that help build replicators.
Comments.UserDisplayName: Neil Slater
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Comments.Text: The simpler, the better. Not interested in modeling on the chemical level. The soup could be a 2D/3D array of integers with arbitrary meaning (e.g. opcodes).
Comments.UserDisplayName: sihubumi
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Comments.Text: Look at Conway's game of life. Simple rules beget replicators like gliders. It's not too much of a leap to see how this may occur in biology.
Comments.UserDisplayName: Ray
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Comments.Text: @Ray: Gliders, although an interesting emergent behaviour, are not strictly replicators. If you put a glider into game of life, the structure changes and re-creates the same structure after a few steps in a different position. It is more akin to movement than replication. Replication would be if you placed an object and it became in a certain number of steps two separate objects with the same structure.
Comments.UserDisplayName: Neil Slater
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Comments.Text: @Neil  One could argue that "movement" is actually an illusion or perhaps movement is a by-product of replication. Nevertheless, since GoL is Turing complete, there is a configuration that does the kind of replication you ask for.
Comments.UserDisplayName: Ray
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Comments.Text: @Ray: Yes there is. I mention one that was discovered in my answer. It is far too complex to be created spontaneously in any practical experiment though.
Comments.UserDisplayName: Neil Slater
Tags: <reference-request><evolutionary-algorithms><artificial-life><self-replicating-machines>
Title: Has the spontaneous emergence of replicators been modeled in Artificial Life?
UserDisplayName: sihubumi
ThreadText: # Has the spontaneous emergence of replicators been modeled in Artificial Life?
  
  (Asked by: username_0 on 2018-10-25)
  
  One of the cornerstones of The Selfish Gene (Dawkins) is the spontaneous emergence of replicators, i.e. molecules capable of replicating themselves.
  
  Has this been modeled *in silico* in open-ended evolutionary/artificial life simulations?
  
  Systems like Avida or Tierra explicitly **specify** the replication mechanisms; other genetic algorithm/genetic programming systems explicitly **search for** the replication mechanisms (e.g. to simplify the von Neumann universal constructor)
  
  Links to simulations where replicators emerge from a primordial digital soup are welcome.
  
  **Tags:** reference-request, evolutionary-algorithms, artificial-life, self-replicating-machines
  > **Comments:**
  > **username_2**: How "soupy" does the primordial soup need to be here? There are no simulators working at level of atomic/chemical interaction. But if we started with higher level building blocks, they are likely to include some rules that help build replicators.  
  > **username_0**: The simpler, the better. Not interested in modeling on the chemical level. The soup could be a 2D/3D array of integers with arbitrary meaning (e.g. opcodes).  
  > **username_3**: Look at Conway's game of life. Simple rules beget replicators like gliders. It's not too much of a leap to see how this may occur in biology.  
  > **username_2**: @Ray: Gliders, although an interesting emergent behaviour, are not strictly replicators. If you put a glider into game of life, the structure changes and re-creates the same structure after a few steps in a different position. It is more akin to movement than replication. Replication would be if you placed an object and it became in a certain number of steps two separate objects with the same structure.  
  > **username_3**: @Neil  One could argue that "movement" is actually an illusion or perhaps movement is a by-product of replication. Nevertheless, since GoL is Turing complete, there is a configuration that does the kind of replication you ask for.  
  > **username_2**: @Ray: Yes there is. I mention one that was discovered in my answer. It is far too complex to be created spontaneously in any practical experiment though.  
  > **username_1**: @sihubumi I'd love to see examples of such simulations too. Were you able to find anything?  
  
  ---
  
  ## 4 answers
  
  ### Answer by username_4 on 2018-10-31. Score: 4
  
  **Systems Approach**
  
  Let's set out to replicate a real time system $S: \mathcal{X} \Rightarrow \mathcal{Y} \; | \; I$, where $\mathcal{X}$ is a empirical continuous history of input and $\mathcal{Y}$ empirical continuous history of output, conditioned upon a real initial system state $I$. Based on some definition, we require $S$ to be alive.
  
  We cannot simulate a replication of a theoretical model of life, with a selfish gene or any other such attribute, simply because no mathematically terse model on which the simulation could be based exists. As of this writing, only hints to and minutia of such a model are known.
  
  Furthermore, models are mathematical representations that, throughout human history, are found to be approximations of complexities once anomalies are addressed and new models develop to incorporate them into the theory.1
  
  **Simulation Roughly Defined**
  
  If we examine a general algorithm $\mathcal{A}$ to replicate $S$, replication can be roughly sketched as follows.
  
  * Estimate system $S$, essentially forming hypothesis $H$.
  * Simulate initial state $I$.
  * Initiate a series of discrete stimuli $\mathcal{X}\_t$ approximating the real and continuous $\mathcal{X}$.
  * Acquire resulting system behavior $\mathcal{Y}\_t$ as discrete observations of $\mathcal{Y}$.
  * Verify the difference between simulated and actual systems to be within allowable error $\epsilon$.
  
  **Defining Spontaneous Emergence**
  
  By spontaneous emergence is meant that such an astronomically large array of initial states and sequences of stimuli occurred that there is a high probability of one of the permutations being alive, based on some specific and reasonable definition of what is living.
  
  **Defining What Life Is**
  
  Reviewing several definitions of living organisms, the most reasonable definitions include these:
  
  * The organism can be distinguished from its environment.
  * The organism can acquire and cache potential energy and materials required to operate.
  * Its operation includes continued acquisition, producing a bidirectional and sustainable relationship with its environment.
  * The organism can roughly reproduce itself.
  * The reproduction is similar to but not exactly like the parent(s).
  * The method of energy and materials acquisition may include the consumption of other organisms or its energy and materials.
  
  Competing for resources, natural selection, and all the other features of evolutionary theory are corollary to the above five requirements. In addition to these, the current trend toward recognizing symbiogenesis as a common theme in the emergence of species should not be dismissed.
  
  * Replication of one organism may be influenced by the composition of another organism through forms of assimilation or symbiosis such that traits are passed across categories of organisms.
  
  **Artificial Life as a Simulation**
  
  These seven criteria poses a challenge for humans attempting to artificially generate life. It is easy to create a computer model such that life is simulated in some way. Consider how.
  
  * The environment contains virtual energy and virtual matter.
  * The model of the organism, distinguished from its environment, can acquire its operational requirements from the environment through a set of operations on it.
  * Mater and energy are conserved because the temperatures are far below nuclear thresholds.
  * The model of the organism allows acquisition only if enough of the energy and materials acquisition has occurred to maintain the cache.
  * Mater and energy acquired by one organism cannot be acquired by another organism except by consumption or absorption of an organism that acquired it or produced it from that which was acquired.
  * The model of the organism can self-replicate in such a way that stochastic differences in the replication is introduced in small quantities.
  * Operational information, including replication information, may be acquired through consumption or symbiotic relationship under some conditions.
  
  **Magical Genes for Spontaneous Life**
  
  Notice that the selfish gene is not mentioned above. Selfishness, the prerequisite of which is intention, is not a requirement for life. An amoeba does not think selfishly when it moves or eats. It operates witlessly. We should not anthropomorphize every organism we study, or develop theory based on anthropomorphic conceptions.
  
  Similarly, symbiotic relationships form that are neither loving nor altruistic. They exist because there is a mutual benefit that appeared as an unintended byproduct of normal operations and both symbiotic parents happened to pass that symbiotic connection to their respective offspring.
  The mutual benefit, the symbiosis, and the replication are witless and unintended.
  
  There need not be a control mechanism distinct from all other replicated mechanisms to control either symbiotic collaboration or competition. They too are natural consequences of living things sharing an environment. Whether an organism dies because it
  
  * Lost its symbiont,
  * Starves because other organisms consumed its necessities,
  * The organism itself depleted its own resources, or
  * Those needed resources were otherwise rendered unavailable,
  
  it is still unable to replicate, so its traits die with it.
  
  Note also that there is no known molecule that can replicate itself. Complex systems of molecules in a variety of chemical states and equilibria are required for reproduction to take place.
  
  **Returning to Simulating an Already Existing Organism**
  
  Running a time sharing system or distributing these simulated organisms in a parallel processing arrangement may some day simulate a biosphere, but it is not one in that only transistor electro-chemistry is involved. There is no actual direct relationship between the energy and mater of the system used to assemble the simulation and the energy and mater of the simulated environment in which the simulated systems $S$ reside.
  
  Certainly genetic algorithms, such as Avida and Tierra, have been developed. Compare those simulations to the modelling scenario described above, and their deficiencies become clear. Human researchers have not yet found $\mathcal{A}$ to replicate $S$ in a way that aligns with biological reality.
  
  **Open-endedness Requires Verification to Have Merit**
  
  The most significant limitation on implementations *in silico*, is that they can never be truly open-ended.
  
  There is no way as of this writing to replicate that which was simulated outside the simulation system. Until nanotechnology reaches a point where 3D construction and assembly can migrate alive simulations into the unsimulated universe, these simulations are closed-ended in that way and their viability *in vito* is untested. The value of open-ended simulations without any way to validate them is essentially zero except for amusement.
  
  Even in the space of digital simulation, as far as that technology has progressed, nothing even close to von Neumann's universal constructor has been accomplished. Although generic functional copy constructors are available in Scheme, LISP, C++, Java, and later languages, such is a minuscule step toward living objects in computers.
  
  **Digital Soup**
  
  The simulation of life's origins is considerably more difficult than finding an algorithm $\mathcal{A}$ to replicate $S$, where $S$ is a single life form and a sufficient portion of its environment to be representative of the biosphere on earth with an organism in it.
  
  The issue with primordial digital soup is one of the combinatory explosion. There are 510 million square Km on the earth's surface, and there are only three categories of life origin time frames possible.
  
  * The current estimates are close to correct, that the earth formed 4.54 billion years ago and extremely primitive life emerged 3.5 billion years ago
  * The organic material found in Canada that is allegedly 3.95 billion years old shortens the gap between planetary formation and life formation on it and older terrestrial life may be found
  * Vladimir Vernadsky's comment that life may have preexisted earth is more than just a possibility
  
  If we go with the 1.04 billion year gap, then $(4.54 - 3.5) \cdot 10^9 \cdot 510 \cdot 10^6$ Km-years of soup must be simulated, since we cannot assume that life started in the ocean or a puddle or even on the surface. It could have started underground or in the atmosphere. The biosphere is currently thought to be 1,800 m above to 8,372 m below thick.
  
  With nanobes being 20 nm in diameter and the possibility that the emergence may have only taken one second we have to simulate in three dimensions over time the following space-time domain in finite elements with at least 50% overlap in all three dimensions.
  
  $$\dfrac {2^3 \cdot (4.54 - 3.5) \cdot 10^9 \cdot 510 \cdot 10^6 \cdot (1,800 - 8,372) \cdot 365.25 \cdot 24 \cdot 60 \cdot 60} {(20 \cdot 10^{-9})^3} \\ = 170,260,472,379 \cdot 10^{9+6+27} = 1.7 \cdot 10^{56}$$
  
  With a quantum computer two stories high the size of Switzerland, the computing time would vastly exceed the duration of the average species on earth. Humans are likely to be extinct before the computation completes.
  
  As the dating of the oldest found fossils converges on the dating of earth, it may seem that life emerged quickly on earth, but that is not a logical conclusion. If life formed as soon as the earth cooled sufficiently and no evidence of continuous emergence is found in the remaining billions of years, then Vernadsky's inference that life arrived on earth through one or more of the bodies that struck it becomes more probable.
  
  If that is the case, then one must ask the question, if all assumptions are dropped, whether life had a beginning at all.
  
  **Simulating Life Versus Simulating Its Formation**
  
  We may simulate what life is, that is, find an algorithm $\mathcal{A}$ to replicate $S$, where $S$ is a single live organism. It is not realistic to, by brute force, simulate how life began without learning more about what conditions can lead to its formation theoretically to drastically reduce the soup simulation space. It is that learning that is an ongoing area of research in the genetic algorithm field.
  
  Early musings about the possibility of an algorithm $\mathcal{B}$, which can provide the conditions that allow an arbitrary organism $S$ conforming to the above definition of life to form with out a parent or parents were interesting. Given algorithm $\mathcal{A}$ that simulates a life form and algorithm $\mathcal{B}$ that simulate the formation of life, it may be the later algorithm that proves significantly more difficult.
  
  Conforming physics outside a computer to the simulation may be impossible. Whether simulated life, when embodied in a robotic system is actually going to be considered life will be left to our descendants, should the species endure sufficiently.
  
  **Footnotes**
  
  [1] Classic cases include the heliocentric Copernican system giving way to the Law of Gravity, that law being shown an approximation of general relativity as shown by the proper prediction of the orbit of Mercury and light's curvature near the sun, the Four Elements dismissed in light of Lavoisier's discovery of oxygen, and absolute provability of truth within a closed symbolic system disproved by Gödel in his second incompleteness theorem and then recouped partially (in terms of computability) by Turing's completeness theorem.
  
  
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  ### Answer by username_2 on 2018-10-25. Score: 2
  
  Although difficult to prove a negative, I don't think that this has been done.
  
  The most advanced simulations of low-level features are not capable of scaling to simulate large enough populations at large enough time scales where scientific consensus claims that this has happened in reality.
  
  Although you say that you are not directly interested in chemistry, but some abstract substrate, I am using chemistry as an example of the challenge. That is because creating a simplified substrate with enough rich emergent behaviour is non-trivial. The chemical elements essentially have rules about how they combine into larger physical structures (via different bonding mechanisms) and only roughly a dozen types of atom are involved. It's actually reasonably simple and tractable at the lowest level. The problems come from the multiple scales of structure - building "unit" molecules (DNA/RNA bases, protein peptides, lipids, sugar bases etc), creating polymers from those units, interactions between polymers, physical structures built and torn down by those interactions, each of which exhibits more complex behaviour. This structural hierarchy is likely required for any self-replicating machinery that is not simply being fed the higher-level units directly. In your question you want to find self-replication that is emergent, not designed . . . so feeding in these higher-level units would probably count as cheating.
  
  We probably don't have the computational power to properly simulate even the [Miller-Urey experiment](https://en.wikipedia.org/wiki/Miller%E2%80%93Urey_experiment) which is far from self-replication - chemical simulations *in silico* are limited to things like protein folding calculations, and these are far from real-time. Inside just a single bacterial cell getting ready to divide, proteins are produced and fold by the hundreds every second.
  
  One thing that has been done is to create a self-replicating machine in [Conway's Game of Life called "Gemini"](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Self-replication). This was designed, not spontaneously created. However, it would have a very low but non-zero chance of spontaneously being created with random initialisation. It would be a very fragile replicator though, any mutation or collision with other active elements would likely break it. The experiment of attempting to randomly/spontaneously create Gemini is not computationally feasible.
  
  It is likely that any physical system simple enough to be considered "primordial soup" yet rich enough to express replicating units is going to require a few layers of construction before you get to see those units. These layers need to be built up combinatorially, and odds of this happening spontaneously in a small experiment with limited computation appear to be low. You need to bear in mind the *extremely large* computation that would effectively have been done by an order of $10^{30}$ molecules that can interact at very fast rates in parallel (compared to rate at which these same interactions can be simulated in current CPUs), with processing times of the order $10^8$ years. It is mainly conjecture that this is enough to create an Initial Darwinian Ancestor - it is basically a logical extrapolation to the theory of evolution, following the Occam's Razor principle of looking for simplest compatible explanation.
  
  
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  ### Answer by username_5 on 2022-04-03. Score: 1
  
  It's yes in cellular automata space, you have this old one from 1997:
  
  *"Emergence of self-replicating structures in a cellular automata space"*
  <http://fab.cba.mit.edu/classes/S62.12/docs/Chou_CA.pdf>
  
  I quote you the part of the abstract you'll be interested in:
  
  *"This article demonstrates for the first time that it is possible to create cellular automata models in which a self-replicating structure emerges from an initial state having a random density and distribution of individual components."*
  
  And those replicators carry some kind of information and are in some minimalistic sense evolvable (the loops can grow).
  But, you'll see the emergence is mainly due to the fact that the cellular automata universe designed allow small replicators, and by just being chaotic enough those replicators form by luck. It's an Langton loop system, you have a live demo there (but quite old as well):
  <https://www.complexcomputation.org/hhchou/research/research_ca_demo1.html>
  
  I dont know any other work that come close to that in term of simulating emergence of replicators, it's old and with limitations but at least it's something.
  
  Regards.
  
  
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  ### Answer by username_3 on 2018-11-01. Score: 0
  
  Primordial replicators can be simpler than you think. Check out this video:
  
  [Self Replication: How molecules can make copies of themselves](https://www.youtube.com/watch?v=w2lqZL153JE)
    
  [Source: University of Groeningen]
  
  In a noisy environment you get natural mutation. And voila, replication + mutation = evolution.
  
  > **Comments:**
  > **username_2**: It's a good link, and relevant to the conversation. However, link-only answers are not considered high quality here. It would be helpful to summarise the video in more detail, and also relate it back to the original question - which is about having this kind of organisation occur spontaneously in a silicon/code environment (whilst the video is a thought experiment which seems feasible for a chemical system).  
  > **username_3**: I actually don't think a summary would help; some things are better shown than explained.  But please feel free to add an answer if you like.  Also, it should be easy to imagine the solution in silico.  Actual implementation details wouldn't add much.  
  > **username_2**: I have already added an answer. If a summary would not help, then please find some other way to make this answer self-contained. It is a goal of the site that question and answer pairs should not *rely* on links. A good way to assess this: If your link stopped working, would the answer still be complete and useful?  
  
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