The Concept of Ruliobiology
Biology is (as Charles Darwin put it a century and a half ago) full of “endless forms most beautiful and most wonderful”. But just where do such forms fundamentally come from? And is there any kind of general theory one can make of them? Darwin seemed to imagine that natural selection alone would (like “the fixed law of gravity”) inevitably lead to such forms. But it’s never been clear just why that would be so. Or how one might in fact set about constructing a theory of such things. But from work I’ve done in the past couple of years, I think we begin to see some possibilities. And that’s what I’m going to be talking about here.
The starting point is what we can call “ruliobiology”. We can think of ruliobiology as a metamodel of biology: an abstract framework not intended to provide a specific model of any particular biological system, but rather intended to capture the essence of certain core features of what’s fundamentally going on in biology. Ruliobiology is ultimately about what happens in systems based on simple rules subject to adaptive evolution—and we can explore it using the general methods and concepts of ruliology.
And what we’ll discover here is that a remarkable range of what we might consider to be “quintessentially biological” phenomena already show up in ruliobiology. And indeed ruliobiology seems to give us a way to see that, yes, in some sense Darwin’s supposition was correct: there is a certain theoretically-derivable inevitability to the generation of ”endless forms most beautiful and most wonderful”.
One of the ingredients that’s needed is indeed Darwin’s idea of natural selection—and the process of adaptive evolution associated with it. But another crucial ingredient is what we can think of as the central phenomenon of ruliology: computational irreducibility. Computational irreducibility is what makes even simple underlying rules very often lead to behavior that is in effect irreducibly complex. And in effect it supplies the “raw material” for ruliobiology—on which adaptive evolution can act. It is then the interplay of adaptive evolution with computational irreducibility that leads to the core phenomena of ruliobiology.
Darwin seems to have imagined that there might be “laws of biology” analogous to laws of physics (like “the fixed law of gravity”). And here indeed we’ll see that there are “laws of ruliobiology”—though they are different in character from laws of physics. For traditional laws of physics tend to concern themselves with aspects of physical behavior that are computationally reducible, and that can be described, say, with mathematical formulas. Ruliobiology—and, I believe, biology—have computational irreducibility at their core. So, for example, whereas in physics one can discuss a phenomenon just as something happening “here and now”, in ruliobiology—and biology—there is an inevitable dependence on history, and on the computationally irreducible process that led us to here and now.
In the past one might have imagined that this would mean there could be nothing general one could say about ruliobiology—or biology—and that everything would have to be attributed just to “accidents of history”. But by thinking about the ruliad and about spaces of all possible rules we discover that there are in fact general things that can be said. One approach is to make use of the concept of the rulial ensemble: the set of rules that are reached by adaptive evolution with some computationally simple fitness function. And the key point is that while the details change with different fitness functions (and different classes of underlying rules), certain emergent features do not—and can therefore be seen as general to ruliobiology.
As is often the case, the introduction of the new methodology of ruliobiology lets us start addressing new kinds of questions—that in many cases one had never even thought to ask before. Ruliobiology is ultimately a rich and vast domain—and here I’ll only begin to scratch its surface. But from what we see here I think it’s already clear that ruliobiology can finally provide the basis for broad theoretical thinking in biology—with the potential to transform how one approaches many important issues in biology.
The Basic Setup
The basic setup in ruliobiology involves looking at “rulioorganisms” that “grow” according to simple fixed rules—with the rules being determined by an overarching process of adaptive evolution. Here I’ll be using rules based on symmetric 5-color cellular automata, grown from “seeds” consisting of a single cell:
The rules (shown on the right) can be thought of as corresponding to the genotype of the rulioorganism; the pattern (shown on the left) obtained by following these rules can be thought of as the phenotype of the rulioorganism. The rules are progressively updated by a process of adaptive evolution—with successive steps of this evolution involving random mutations that change the outcomes for particular rule cases:
The mutations are preserved if they increase (or at least leave constant) a fitness function; otherwise—in an analog of natural selection—they’re rejected. The particular fitness function we’ll mostly use here is “lifetime”, defined as the number of steps for which a phenotype pattern survives before dying out. (We take infinite patterns to have zero fitness.) With this setup we can plot (as red dots) the fitness values obtained by a sequence of mutations:
We see that many mutations decrease fitness—which means they’re not preserved. But every so often there’s a “breakthrough” that increases fitness. And looking at the rulioorganisms corresponding to these breakthroughs we see—a bit like in the fossil record—that they involve a sequence of “discoveries” that build on one another to progressively increase the fitness:
It’s immediately striking how “biological” these patterns look—with lots of complexity, but also identifiable patches of regularity reminiscent of the structures like organs that we see in biology.
The particular rulioorganisms in the picture above are the result of a particular sequence of random mutations. As we will soon see, other sequences of random mutations will lead to quite different rulioorganisms. But despite their detailed differences, what we’ll find is that there are features of these rulioorganisms—and their evolution—that are widely shared, and in effect represent the core phenomena of ruliobiology.
The Forms of Rulioorganisms
What can rulioorganisms be like? Here are a few examples:
The resonance with Darwin’s “endless forms most beautiful and most wonderful” is certainly striking. Each of these rulioorganisms was ultimately evolved with the same simple objective of “living as long as possible”. But what we see is that the rulioorganisms achieve this objective in a remarkable diversity of different ways. Notably, not a single one of these ways is “simple”, in the sense that one can readily give a simple “mechanical” description of how it works. And at some level all of them “just happen to work”, in the sense that they represent frozen pieces of computational irreducibility that turn out to achieve the objective—even though one can’t see that this will be the case except in effect by explicitly running them and observing what happens.
So how did these rulioorganisms evolve? Here are some examples of the sequences of breakthroughs that were involved, in all cases starting from the trivial “null” rule:
The details are different in each case. But there’s an important common theme. In the course of the adaptive evolution, some “innovation” is invented (like “use triangular regions of purple”), and then, as the adaptive evolution proceeds, this innovation is progressively (and often “creatively”) elaborated.
Novelty at Every Scale and the Phenomenon of Polyplexy
Look at a biological organism at different scales and you’ll see different things. Indeed, it seems as if in biology there’s—quite ubiquitously—“novelty” at every scale. When biological organisms were first examined under microscopes it was a big surprise how much unseen structure was discovered. And with essentially every new level of microscopy that’s introduced, yet more—often very different—new structures seem to be revealed.
Nesting and the idea of fractals captures the notion of having smaller copies of the same structure at different scales. But what we’re talking about here is something very different: we’re talking in effect about having a whole hierarchy of novelty, where fundamentally different things are happening at each scale. It’s something that’s been hinted at—particularly in biological contexts—for centuries. But so far as I know, it’s not something that’s ever explicitly been given a name. Here I’ll refer to the phenomenon as polyplexy. (As we’ll discuss below, it’s a different phenomenon from what one sees in something like the Mandelbrot set.)
So do we see polyplexy in ruliobiology? The answer is yes, quite ubiquitously so. Consider for example this rulioorganism:
What we probably first notice is its complicated overall shape:
Next we might notice its areas of purple—and the random-looking “connective tissue” between them. But let’s zoom in a bit, say near the lowest part of the pattern:
There are areas of purple alright. But they’re laced with (irregularly placed) vertical stripes. And we can now see that the connective tissue isn’t really random: there’s actually all sorts of structure in it. Zooming in a little more (and showing only the left half of the pattern) we start to see a whole variety of specific highly ordered structures dotted around:
At a still smaller scale we begin to see how those structures are embedded in the larger pattern:
And zooming all the way down to “ruliological atoms” we can finally identify some of the “lowest level structures” in our rulioorganism:
We can think of such structures as corresponding to patches of computational reducibility. But sometimes—even at the lowest level—there’s just too much immediate computational irreducibility for us to be able to discern any kind of “describable structure”:
Looking at our rulioorganism as a whole, we see that—like a typical biological organism—it contains many small structures that are basically repeated in different places
though often in slightly different forms:
Biological organisms are typically viewed as having a hierarchy of types of parts (from organ systems to organs to tissues to cells to organelles, etc.) And one might have imagined that cellular automata of the kind we’re using here—with their simple, uniform underlying discrete structure—would never be able to exhibit any such hierarchy. But in fact we find that our rulioorganisms are full of hierarchy—usually with visibly different kinds of structures on different scales:
Another feature of rulioorganisms is that their different parts are often differentiated from each other. In the end, the parts must all “work together” to achieve the fitness objective that’s been defined. But in general, many of them will in some sense “do different things”—much like different parts of biological organisms.
(It’s useful to contrast this with what happens in something like the Mandelbrot set, where there’s plenty of visual diversity, but where at every coordinate position and every zoom level one’s just seeing geometric distortions of a single object, with the distortions defined essentially by the digit sequences of the coordinates.)
The Diversity of Rulioorganisms
We saw above various examples of rulioorganisms. But what is the space of all possible rulioorganisms like? I’ve argued elsewhere that any “rulial ensemble” of what we now call rulioorganisms selected according to any computationally simple fitness function will have certain overall features in common. But to be specific here, let’s start by considering (symmetric) rules selected purely on the basis of lifetime, and let’s look at the rulioorganisms we get after 1000 steps of adaptive evolution (here with the lifetime in each case indicated):
As we’ll discuss later, our process of adaptive evolution is fundamentally open ended, and by continuing it we can expect to find rulioorganisms with longer lifetimes. But for now, let’s just impose the criterion that the lifetime after 1000 steps of adaptive evolution has to be above 500:
There is a certain sameness to the overall appearance of these rulioorganisms—perhaps much as there is a certain sameness to the overall appearance of a great many species of biological organisms. But the distribution of possible forms of rulioorganisms is broad, and selecting for “visual impact” (measured, say, on the basis of width and compression size) one gets some more exotic examples, including many quite unexpected forms:
(Later we’ll discuss the convergent evolution that we can see here.) It’s perhaps notable that among rulioorganisms one typically finds that “visually exotic” ones arise at the level of a fraction of a percent—perhaps not so different from the level of visually exotic fish or other species typically on display in aquariums, etc. (And, yes, the fact that one can even imagine saying something scientific about a topic like this is remarkable, and a sign of the fresh and different paradigm that ruliobiology introduces.)
One might have assumed—in a natural selection kind of way—that to get exotic forms one would need an exotic environment, and exotic fitness function. But what we’ve seen here suggests that exotic forms can actually arise—albeit rarely—without an exotic fitness function, in effect just as examples of “surprises” that can inevitably be created by computational irreducibility.
Extreme Rulioorganisms
We’ve talked about typical rulioorganisms. But what about extreme ones?
To be specific, let’s look at a sample of 100,000 rulioorganisms randomly generated by 1000 steps of adaptive evolution, with lifetime as the fitness function. In terms of largest lifetime, the most extreme rulioorganisms in the sample turn out to all look rather similar:
But what about in terms of other attributes? The rulioorganisms with the largest maximum widths are, for example:
And one thing that’s notable here is that many—but not all—of these rulioorganisms use the same “pincer” strategy to achieve their large width. The details are different. And (as we’ll see later) the paths by which these rulioorganisms were reached are different. But their forms they achieve are very similar.
By the way, if we rank in terms of width/height, rather than just width, then we get many of the same extreme rulioorganisms (at least so long as we exclude rulioorganisms with very short lifetimes):
If we ask instead to minimize width/height then we get:
We see a whole range of different “ideas” in use here—though several seem to work by showing a certain kind of “almost periodicity”, at least for a while. Closeups reveal a little more of what’s going on:
As another example, we can look at rulioorganisms that have the largest total number of non-white cells (relative to lifetime):
Closeups reveal somewhat different mechanisms at work (the “filling” in the first two cases, for example, corresponds to 2-color cellular automaton rules 182 and 126):
Here are rulioorganisms with the smallest number of non-white cells relative to their “bounding box” (i.e. width × height):
What about rulioorganisms that are (in our rendering), say, “extremely green”? Here are rulioorganisms that have the largest number of green cells relative to other colors:
And here are the corresponding results for red—slightly different because the random mutations we chose did not happen to explore the “red analogs” of exactly the “green rules” above:
If we ask for extreme red+green we often get just “extreme red” or “extreme green”, but sometimes we get “new ideas”, like alternating stripes or more complex patterns:
How common are extreme rulioorganisms? Across all possible rules, here are the distributions of values for the attributes we’ve been discussing (all shown on a log scale):
We see a variety of overall distributions, some exponential, some not. But all of them exhibit tails—which is where the exotic rulioorganisms are. Remember that here we are selecting only for lifetime. So any extreme values of other attributes are in a sense just “side effects”. And what we’re seeing is that “extreme side effects” appear to be a ubiquitous phenomenon in ruliobiology.
In traditional evolutionary biology, there tends to be an assumption that organisms with extreme traits arise because of selection associated specifically with those traits. So let’s say we’re looking at maximum width as a trait. Adaptive evolution using width as a fitness function yields for example these “fittest rulioorganisms”:
And what we see is that the widths achieved in this way are somewhat larger than the ones we got just as side effects, but not dramatically so. In other words, explicit adaptive evolution for a particular trait doesn’t seem to be getting us much more extreme values of that trait than we would get just by looking for this trait as a side effect. In essence, at least when it comes to extremes, the intrinsic “element of surprise” that exists in ruliobiology (and that ultimately results from computational irreducibility) is essentially just as strong an effect as specific adaptation.
The Shapes of Rulioorganisms
How can we characterize the “shapes” of rulioorganisms—say as defined by their outer boundaries:
Stacking up a large number of these boundary shapes we get the following “average shape”:
The main part of this grows roughly like 
—just as we would see for a collection of random walks. But the boundaries are definitely not in fact “random walks”; for example, while they can expand by at most 1 cell (on each side) at each step, they can contract by any number of cells—with the distribution of contractions being
or about 
.
A notable feature of our boundary shapes is that they usually show a certain roughness. To characterize this we can see how the total length of approximations to the boundaries varies (“coastline-length-style”) with the size of straight segments used to make them:
Fitting the resulting total lengths to a power law, we can deduce an effective fractal dimension, which in this particular case is about 1.35. Looking at many boundary shapes, we find that the distribution of fractal dimensions is very roughly Gaussian, with a mean around 1.3:
If we look in detail at the boundaries of our shapes one thing we’ll see is that they always have sections that are periodic—with fixed (rational) slopes:
And we can use the frequency of repeats of different slopes to provide a kind of “boundary signature” for our shapes:
But what about finding a general way to characterize the overall shapes of rulioorganisms? It’s not an easy problem, mathematically or otherwise. And in ordinary biology even simple analogs of it have proved challenging. Occasionally—as in the case of mollusc shells—there’s a continuous range of shapes, say determined by a growth parameter in a differential equation. But more often one ends up just with a taxonomy—in which classes of forms are named, often by analogy with everyday objects, as for example in the case of leaf shapes:
And, yes, for what it’s worth, we can do something similar with our rulioorganisms, say using an LLM:
Rulioorganism Anatomy
We’ve talked about the outer boundaries of rulioorganisms. But what about their internal structure—their anatomy? Something that’s remarkable is how many general features of this structure are similar to what we see in biological organisms. At the simplest level, we can think of rulioorganisms as consisting of regions of tissue interspersed with “voids”—shown here as white:
There’s a lot of diversity in the overall “topology” of the “tissue”:
And there are several very different types of “tissue”. Sometimes there are patches of pure periodicity:
Sometimes there are patterns with pure nesting:
Sometimes there are regions of typical class 3 cellular automaton behavior enclosed within boundaries:
And, yes, what might at first here seem like uniform diamond-shaped patterns are actually full of class 3 behavior:
But perhaps the single most striking feature of most rulioorganisms is the presence of repeated modular structures that seem somehow “functionally separated”—in a way that’s reminiscent of organs, organelles, etc. in actual biology:
Sometimes these structures are delimited by highly regular “skeletal” elements:
But often the boundaries show considerable randomness:
And in fact there are often whole regions of randomness
that separate modular structures:
One can think of these regions of randomness as representing a kind of “connective tissue” between organ-like structures. And what’s remarkable is that this mirrors what one sees in actual biology. In some sense we can see this as a case where ruliobiology—on purely abstract computational grounds—can in effect “derive” an important, though typically unspoken, feature of biology: the presence of distinct “connective tissue” that separates organized structures, but is itself seemingly quite random.
(By the way, at a medical level, the randomness of connective tissue can be seen as an important part of what makes surgery possible—because it’s this randomness that allows connective tissue to be rearranged, yet still achieve its function.)
Parts and Wholes in Ruliobiology
Biological organisms tend to operate only as integrated wholes; their parts typically don’t usefully work in isolation. And so it also is with rulioorganisms. For example, imagine a patch in the pattern corresponding to a rulioorganism. Now ask what happens if we take the configuration at the top of that patch, and run it in isolation. Typically what we find is that in isolation the part behaves very differently from how it does in the whole:
Here are some other examples:
There is, in effect, widespread bulk orchestration in which everything is orchestrated to work together, with parts on their own not doing what they do in the whole.
We can think of rulioorganisms as being “frozen pieces of computational irreducibility” that “just turn out” to optimize certain fitness objectives. And from this point of view, the fact that a rulioorganism forms an “integrated whole” where “everything matters” can be thought of as reflecting underlying computational irreducibility. Just as you can’t reduce computational effort by jumping ahead and skipping everything in between, you also can’t reduce it by considering only a limited patch of underlying cells and ignoring everything else. Or, put another way, there’s an irreducible need to include the context of the whole rulioorganism to get the parts to behave as they do in the whole rulioorganism: there’s no systematic shortcut one can take.
There’s something else as well: in ruliobiology—just like in biology—adaptive evolution ultimately operates on whole rulioorganisms. And this means that not only do the parts of a rulioorganism build up to determine the behavior of the whole rulioorganism, so also—because it’s what adaptive evolution operates on—the whole rulioorganism in a sense determines the forms of its parts. One way to describe it is to say that the parts define the mechanism that builds up the whole, while the fitness of the whole defines what one can think of as a purpose for it.
This interplay between parts and whole—and purpose and mechanism—seems to be something very characteristic of what we see in biology. But now, in ruliobiology, we can see its fundamental origins: it’s all about the presence of computational irreducibility and its interplay with the computational boundedness of fitness functions of the kind used in adaptive evolution.
Open-Ended Ruliobiological Evolution
We’ve seen many examples of remarkable forms produced by adaptive evolution—here for 1000 steps:
But what happens if we just keep going with our adaptive evolution? Do we continue to get “even fitter”, and perhaps even more remarkable forms? Here’s what happens if we go another 1000 steps in this particular case:
The increase in fitness has “kept going”, here achieving a final fitness (i.e. length) of 1445—nearly 2.5 times the 580 achieved after 1000 steps. Can we go even further? With a fixed number of discrete elements in the rule (i.e. ruliogenome), we’ll eventually “hit the edge of rule space”. But if, for example, we not only change the rule, but also change the size of the initial conditions, we’ll get an indefinitely large number of cases—and we can expect that we’ll have entirely open-ended evolution, that can eventually reach arbitrarily large fitness. In other words, with this setup, there’ll normally never be a “final best rulioorganism”; in effect, there’s always something better to be found somewhere in the ruliad.
The example above illustrates a typical phenomenon: that as the process of adaptive evolution goes on, it’s continually “reusing ideas” (like here of having large patches of purple)—but progressively refactoring and embellishing them.
Occasionally in the “ruliological fossil record” one will see a kind of alternation between rather different boundary forms—even as many of the same features are maintained inside:
Here’s another example that again illustrates “reuse of ideas”, but “refactored” into a sequence of forms that—if one didn’t know their “ruliogenetic” connection—might seem rather hard to relate:
Convergent Evolution in Ruliobiology
In the evolution of life on Earth a repeated phenomenon that’s observed is that some feature of organisms—like eyes or wings—arises independently multiple times, by different routes. The same kind of convergent evolution also happens in ruliobiology. For example, here are four different ways “green pincers” can arise:
The main features of at least the pincer part of the final morphology are the same each time. But the way this morphology was reached is different. There are in effect multiple different “origin stories”, all converging on the final feature of green pincers.
Here’s another example, now of generating patterns with overall diamond-like boundary shapes:
And here again the paths of evolution are different—even though they “converge” to give the same overall final boundary shapes.
(What we’re looking at here is approximate convergence, to qualitatively similar forms. It’s worth noting that in a discrete rule space there will always be adaptive evolution paths that lead to exact convergence—and indeed we looked at this previously in much smaller rule spaces using multiway systems.)
Side Effects in Evolution
When we adaptively evolve on the basis of a particular fitness function, what other traits will our rulioorganisms also end up having? In other words, what are the “side effects” of particular adaptive evolution? For example, if we evolve to maximize lifetime (as we’ve been doing here), then does this mean that we’ll inevitably produce rulioorganisms that also have some other—perhaps seemingly unrelated—identifiable feature?
As a very simple example, we can ask what maximizing lifetime (i.e. length) implies for the widths of patterns. Do patterns that are longer also tend to be wider? Or do they tend instead to be narrower? Running 100,000 cases of adaptive evolution (each for 1000 steps) we see that there is in fact a general trend for longer lifetimes to be associated with greater widths\[LongDash]or, in other words, for maximizing lifetime to have as a side effect an increase in width:
If we instead explicitly maximize width, we see that the widths we get can sometimes be larger than the ones that arose purely as side effects:
But the effect is not all that dramatic. And so—in a phenomenon that’s important in thinking about explanation in biology in general–if we just see a rulioorganism with a large width we can’t reasonable conclude that it’s that way because of direct selection for width; its large width could just be a side effect of selection for something else.
And in general lots of things can arise as side effects. Indeed, we can ask about any trait that we can systematically measure, and how it is affected by adaptive evolution for any other trait. Or, a little more formally: if we do adaptive evolution with some computationally bounded fitness function, how will this affect some other computationally bounded function that we can measure? Sometimes there may be obvious connections between such functions (typically associated with the basic forms of the rules for rulioorganisms). But the difficult issue is to understand the inevitable non-obvious connections, say associated with the structure of ruliobiological space, and with relations between different pockets of computational reducibility.
The Correlation of Traits
If a rulioorganism ends up having one trait, does that make it more—or less—likely that it’ll end up having some particular other trait too? One might imagine that perhaps one could develop some kind of “algebra of traits” that would describe what can occur with what. And when it comes to extreme traits, one might imagine a “theory of monsters” that would tell one, for example, what science-fiction-style chimeras can plausibly arise from adaptive evolution, and what cannot.
As a first example, let’s consider rulioorganisms generated as usual by adaptive evolution with lifetime as a fitness function. Now we ask how many red cells and how many green cells such rulioorganisms contain:
We see there are outliers with many red cells, and ones with many green cells. But—at least in this sample—there aren’t any “red-green chimeras”, with large numbers of both red and green cells.
What about yellow and green, though? As so often in the ruliological world, there’s a surprise: a rulioorganism with both many yellow and many green cells:
One might think it would have something like a simple pattern of stripes. But no. It’s contained class 3 behavior that happens to have both lots of yellow and lots of green:
And, yes, it’s a feature of the open-endedness of ruliobiological evolution that one doesn’t get traditional forms of “Pareto frontiers” with tradeoffs between traits. Instead, as in this example, there can be outliers that “open-endedly” in essence “win on all counts”.
But insofar as what we consider “traits” correspond to computationally bounded properties of rulioorganisms, we can think of correlations between traits as being associated with maps of connections between pockets of computational reducibility in ruliobiological space. At some level it’s inevitable that such connections must exist, defining what amount to laws about the forms of rulioorganisms. But the phenomenon of computational irreducibility implies that in general there will be no immediate way to know what such laws will be. And in effect there will be no choice but to do what amounts to experimental ruliobiology to try to find them.
Conservation of Development in Rulioorganisms
Even when the final forms of evolutionarily related organisms look completely different, it is typical in biology for their early stages of development to nevertheless look very similar. So what’s the story for rulioorganisms?
Here’s an example showing the first 30 steps of development from the seed, together with the final form of each “evolutionary breakthrough” rulioorganism:
We see that the early part of development quickly becomes very similar. It’s as if in the process of adaptive evolution the problem of “how to start” gets solved early, and is then kept constant, even as later adaptive evolution adds “embellishments” that affect later development, though not “how to start”.
But what is the underlying mechanism for this? The essential point is that—at least in this example—only a subset of rule cases are used in early development, and while these remain constant, so does early development. In our particular example, the first 10 steps of development are what end up becoming “conserved”:
Showing the outcomes for each rule case in successive “breakthrough rules”, and highlighting the rule cases that are actually used in the first 10 steps of development, we see that after a little while just a fixed collection (58 out of 125) of the rule cases get used:
Doing the same computation for 30 steps of development, the set of rule cases used doesn’t “freeze” in the same way—with the result that if we look at 30 steps of development, we’ll get results that change in the course of adaptive evolution:
What about other “lineages” of adaptive evolution? Here are a few examples:
In all cases the first very few steps of development are conserved. But the number of subsequent steps that are conserved is different in different cases.
In some sense, one can think of conserved behavior as reflecting the notion that adaptive evolution is “coming up with an idea and then sticking to it”. Different paths of adaptive evolution “come up with different ideas”. But along one path one can imagine that ideas are somehow typically conserved, and progressively built on.
Eventually one may hope to have a general characterization (and perhaps theory) of this “progression of ideas”. But, for now, that is something for the future.
Divergence and Persistence in Evolution
Let’s say we’ve done some adaptive evolution, and reached a particular rulioorganism, like:
Now we can ask: what happens if we continue our adaptive evolution from here? Inevitably there are a large number of possible paths this could follow, each corresponding to a particular sequence of random mutations made to the underlying rule. But as an example of what can happen, here are the next rulioorganisms found by following a few of the possible paths:
The random mutations on these different paths happen to make two pairs of these rulioorganisms precisely identical. But in general—despite a certain overall similarity—there’s definite divergence between these rulioorganisms.
Go another step along each path, and the divergence begins to increase substantially:
After another step, it’s starting to be less obvious that these came from a common ancestor:
Allow a total of 1000 mutations on each path, and we reach rulioorganisms that are more typical of all possible rulioorganisms—though still with distinct indications of their origins, like a continuing predilection for purple:
Here are a couple of other examples—again showing that once there is recognizable structure, it tends to get carried along throughout the process of adaptive evolution:
In other words, while starting from something like the null rule yields tremendous possible diversity in rulioorganisms, that diversity is greatly curtailed once there’s “commitment” to a certain general form.
So, for example, this shows the trajectories with respect to fractions of red and purple starting both from the “committed” rulioorganisms above, and from the null rule:
In effect what’s happening is that the further the adaptive evolution has progressed, the more commitment there is, and so the tighter the bundle of trajectories becomes—and the more memory of the starting point persists:
Inevitability and Historical Reconstruction in Evolution
If adaptive evolution is going to produce a certain form, how inevitable is it that it must have gone through a particular precursor to get there? (It’s like asking in biology: if one’s going to evolve legs, does one have to have evolved fins first?)
We saw above examples of the phenomenon of convergent evolution where there are very different paths that lead to a given general form. But is this the exception, or what’s typical? Here are some possible one-step precursors of particular rulioorganisms:
And while there’s a fair amount of morphological diversity in these predecessors, they do at least share certain coarse features—like where roughly they lie in the space of color fractions:
And even “rewinding evolution” back to its very first breakthrough, we still see a certain clustering in color fractions that reflects “where the evolution will end up”:
In other words, even at the earliest stages of adaptive evolution there’s already a fair amount determined about where the evolution will end up. Or, put another way, there’s a fair amount one can deduce about features of even distant ancestors from the form of an evolved rulioorganism.
But let’s say we know the color fractions for a rulioorganism. Typically there are lots of rulioorganisms with very nearly identical color fractions:
And if we look at successively more predecessors of these, we see they quickly diverge in color fraction space:
In other words, knowing just a coarse feature like color fractions is not enough to be able to successfully “retrodict” what happened in the process of evolution; one needs more detail. Or, put another way, there’s no simple “law of motion” for ruliobiological evolution, that talks only about color fractions.
What Does Ruliobiology Mean for Astrobiology?
The basic goal of ruliobiology is to capture certain essential features of life. But in operating as it does at a very foundational level it has the potential to capture not only life as it is here and now on Earth, but also life as it can be, in generality. And in this sense we can think of ruliobiology as providing a new theoretical basis for astrobiology—that lets us discuss in a systematic way what characteristics potential instances of something like life might have elsewhere in the universe.
In formulating ruliobiology we already assume certain core features of what we think of as life, in particular the “code=data” phenomenon (presumably implemented through self-reproduction) of having an underlying rule where the results of running that rule affect the subsequent form of the rule. Elsewhere I have argued that with this adaptive evolution setup, computationally simple fitness functions inevitably pick out a certain rulial ensemble of possible rules, that lead to rulioorganisms that share certain important general features.
Here we’ve looked in more detail at rulioorganisms obtained with a specific setup. But—particularly in view of our results about rulial ensembles—we can expect that many, if not most, aspects of what we’ve seen will actually be quite general to rulioorganisms of any type.
And this means that we can have some confidence that our results will be relevant for astrobiology, as well as, for example, for understanding previous and alternate forms of life on Earth. So what do we learn from ruliobiology for astrobiology?
Perhaps the most immediately actionable result is an essentially visual one: we’ve seen that rulioorganisms tend to have certain characteristic visual features—essentially manifestations of mechanoidal behavior in which structured, modular parts are visible within overall complexity. And we can anticipate that these kinds of forms are also what one should expect in astrobiology.
Another central result in ruliobiology is that there’s a great diversity of forms for rulioorganisms—and again we can anticipate that this will carry over to astrobiology. And, in a sense, we must expect the unexpected: we must expect to see exotic forms that lie far out in distributions we might try to construct.
No doubt some of these features will apply not only to overall morphology (as one might see with a microscope in a physical specimen), but also to molecular-scale structures and processes.
But the key point is that ruliobiology—and the concept of the rulial ensemble—leads one to conclude that there are definite signatures of extended processes of adaptive evolution. In other words, just by looking at features of what comes out, one can get confidence that there was a long, arduous and computationally irreducible process of adaptive evolution underneath, that one can think of in its computational essence as being as being like what happens in the evolutionary development of biological life as we’re familiar with it.
From Darwin to Ruliobiology…
Almost exactly 100 years before I was born, Charles Darwin ended his Origin of Species with
It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.
So what can we now add, with ruliobiology, to what Darwin said? For a start, Darwin seemed to imagine that—like the law of gravity—there would be a fundamental law that causes “endless forms most beautiful and most wonderful [to be] evolved”. We’ve never before had any kind of general or formal way to talk about biological form. But now, with ruliobiology, we do. And we can confirm that—as Darwin suspected—there are indeed general principles at work that lead to diverse and complex forms. But those general principles need something beyond what Darwin knew, or imagined: they need ideas that are fundamentally computational, and ruliological.
In what he wrote, Darwin in effect asserted that the appearance of forms such as those of “higher animals” would “directly follow” from the “war of nature” and the mechanism of natural selection. But despite often strident claims to the contrary over the past century and a half there’s never been a clear picture of how this would work. Yes, one can see that natural selection can lead to adaptive evolution. And one might imagine that the complexity of the ecological environment would somehow be imprinted on the forms of organisms and lead to the kind of diversity and complexity we see. But there’s been no formal theory that shows us this.
And what ruliobiology now suggests is that actually there’s a quite different driving force at work: the phenomenon of computational irreducibility. And indeed the picture that emerges is that the core features of biological form are instead in many ways just frozen fragments of computational irreducibility, in effect assembled and selected by adaptive evolution. The complexity—and diversity—that we see in biology is, more than anything, a reflection of intrinsic, fundamental computational features of a system that, in Darwin’s words, shows growth, reproduction, inheritance and variability. And this is something very robust; it doesn’t depend on the details of the system, so that even without knowing all those details, we can start building a rich and broad theoretical framework. Which is what ruliobiology aims to do.
In the course of this piece, we’ve seen a whole variety of phenomena associated with ruliobiology—many of them reflected in features of biology and biological form that had rarely, if ever, even been systematically discussed before. There is much to do in ruliobiology, and we are still at the very beginning—surveying as an analog of natural history the world of rulioorganisms, and starting to see some general principles emerging. Over time we can expect to see a whole formal tower of theory develop, eventually in scope perhaps within striking distance of physics, but very different in character—and with computational irreducibility, rather than computational reducibility, at its core.
Darwin took pains to emphasize his perception of the “grandeur” of his view of life. But for us, there is, in a sense, still much greater grandeur. For through ruliobiology we can now see just what kind of computational process is needed to build up the kind of richness we see in biological form. There’s computation going on throughout the physical universe—all ultimately encapsulated in the ruliad that represents the entangled limit of all possible computational processes. But ruliobiology—and presumably biology—corresponds to a certain coherent slice of the ruliad, in effect picked out by adaptive evolution. And to reach life as we know it we now realize that we need an immense and irreducible tower of computation. Indeed, we might even say that as living organisms we are the product of the largest coherent tower of computation that we know or can currently imagine.
Darwin spoke of the richness of life as being the result of “laws acting around us”. A century and a half later I believe ruliobiology begins to fill in the essence of what those laws might be. It also opens up a vast new domain of theoretical science—a different theoretical basis for a science of biology. I’m excited to have been able to take some first steps in ruliobiology here. But there is much still to investigate and discover, and I shall look forward to seeing ruliobiology develop, and move towards taking its place among the major theoretical frameworks of science.
Further Reading
“Foundations of Biological Evolution: More Results & More Surprises” (2024)
“What’s Special about Life? Bulk Orchestration and the Rulial Ensemble in Biology and Beyond” (2025)
“Towards a Computational Formalization for Foundations of Medicine” (2025)
See also the historical notes in my earlier writing.
Thanks
Thanks to several researchers at the Wolfram Institute for their help, particularly Willem Nielsen, Júlia Campolim and Pedro Marquez-Zacarias, as well as Adelina Torres Ochoa and Nora Popescu.
