Basins, Evolutionary Leaps, and Morphogenesis:

The zebra stripe pattern

E42 is designed primarily to address issues in human epistemology. To understand how it might do so, especially in the context of Bateson's equating the processes of evolution with those of learning, requires how models of this type might provide insight into evolutionary princesses. Consequently this page will on the surface address current issues the conversation about how evolution works. The question running the the background is how is this like how knowing works?

The applet below allows you to play with variables that generate experiences which will give you insight into Alan Turing's central ideas in his landmark "Morphogenesis" paper. These variables will also provide a basis for understanding how natural selection and self-organization (emergence) might work together to shape the course of evolution.

You will be able either to perturb a system massively by changing the value of, say, 50% of its nodes or to perturb it delicately by change only 1% or 2% of its nodes. Changing a small percentage of nodes may require many perturbations before you see a basin shift. Perturbing a few nodes simulates how it is possible that a change in the allele value of a few genes can provoke a profound change of form.

Detailed Instructions for using the the applet.

FIRST Set the "Window Size (Iterations)" slider to any value that is not a factor of 5. For example Window Size = 69 works well.

Note: The longer the window size, the slower the program will run. If your computer runs the applet slowly use a Window Size in the order of 24 or 29.

[Optional: If your computer runs the apple too quickly (output is a blur on the screen), check "Use Delay" and use the Slider to set the "delay between iterations" to about 10 ms. If the your computer runs the pattern too slowly, uncheck "Use Delay." ]

Press Play (Green Arrow).

Experiment 1.
Perturb the system. Press the Perturb button with the default 50% node perturbation. This will typically shift the zebra stripe pattern to a different pattern. Do this several times.

Notice Basin Structure. As you perturb the system several time, you might notice that this system has eight basins, including a white (albino) and black form. These two are both length L=1 and are unlikely to occur so you might not see them. The other six basins (all L=5) take on a striped form that is evocative of animal camouflage. Notice that the changes in form occur suddenly without a slow, winding "random" walk via a process like natural selection.

Experiment 2. Play with the Percentage of Nodes Perturbed. Massive changes in the the system are typically overkill and not necessary. It is instructive to select 1% or 2% of nodes to be changed in a single perturbation. Is is plausibly how small genetic shifts might happen due mutation (e.g., to environmental influences such as cosmic rays, chemicals, etc.). Most such small changes in the genome would produce no effect. But every once in a while a small change will produce a large effect, a leap into another basin. You may have to click the perturb button quickly and repeatedly in order to provoke a change of basin.

Highly-focused, deterministic changes. E42 has tools that allow us to find the one (or the few) nodes which need to be changed to provoke a particular change. This is a deterministic system so it is possible to track down the exact perturbation that produces a given effect. Sometimes an effect requires changing a few nodes, other times it can be provoked by changing the state of a single node. In effect we can say that perturbing the value of node X on iteration Y will provoke a shift from basin A to basin B. These tools are not included here and are beyond the scope of this page. The idea is, however, that small, specific changes can provoke large changes in the form of a system. A complete analysis of this logic for a simple system is provided in the tutorial where we saw that changing a single value of a node would change the system from basin Beta to basin Gamma.

The Interplay of the processes of Natural Selection and Self-Organizing Form. A single, focused perturbation can provoke the system to produce very different kinds of camouflage. Kauffman's (1993) theory proposes that evolution is shaped by two processes, self-organized emergence of form (morphogenesis) and natural selection. Experiments 1 and 2, which demonstrated a sudden shift of form from one striped pattern to another, simulates the contribution of self-organization to evolution. Concurrently, in a ecological context, natural selection would be working in conjunction with self-organization: Which of the various camouflage patterns (found in Experiments 1 and 2) would survive in a given context? That would be shaped by natural selection. For example if night migration became desirable, the rare black camouflage would be more functional than other patterns. Those other patterns would be selected against in the context of night migration because predators would kill more of the young and vulnerable beings with those striped fur patterns before they could reproduce. In contrast, if a snow adaptation became desirable, then the rare white pattern would be more functional in that context than other patterns, particularly than the all black pattern. The black and the striped patterns would be selected against. In the context of a particular kind of change of context in vegetation color, one of the striped patterns might be more functional and other patterns selected against.

Natural Selection is a theory about how various pressures act on a whole population to shift the statistical occurrence of particular gene patterns within that population.
Morphogenesis (Self-organized form) is a theory about how the actual ontological form (e.g., camouflage) comes into being in a given existential being. Suppose that a genetic change occurs in a particular being due to mutation or recombination (e.g., sexual mixing of genes). What form will that being take? Self-organizing processes inherent in the interplay of processes within that being will determine which particular pattern of form emerges. Later, selective pressures of a given environment will determine if the the being who has assumed that form gets to reproduce or not.

Notice here that the massive shift of design from one basin to another is done deterministically by the interplay of the variables of the dynamic system that determine the existence of the basins. This is kind of process Turing's Morphogenesis paper addressed in a pioneering way. There is no Homunculus nor is there a Great Designer. Nor does natural selection need to be overburdened to account for the creation of the designs themselves because the designs as Turing proposed are inherent in the recursive interplay of the variables that define the structure of the system. Natural selection only has to select against designs that function poorly in context.

Experiment 3. Standing Waves for Basin Length L=5. Turing found that in certain phase relations among the variables whose interplay generates form determine whether the resultant form is a standing wave or a moving wave. We can now gain some experience with that distinction. If you set Window Size to factors of 5 (10, 15, 20, ...), you will see what appears to be a static image. It is not. If you check the iterations per second (ips) you will notice that your computer is running the dynamic system at some high rate; and, whatever that rate of the process may be, it has been tuned in a way that stabilizes pattern. If you set Window size to some other factor of five you will notice that the your computer is producing that standing wave at a different speed (fps). Like all living process, the process must be ongoing to maintain the "thing." A person may appear to be a thing, even to be static, in many aspects, but obvious people are not static. Ending even on essential process, e.g., cardiovascular functioning ends the person. All the processes are required to run and interact to produce stability.

Instead of moving dynamically as a the camouflage pattern did when you set Window Size to values not equal to factors of 5 (above) it now appears static. Common examples of standing waves are waves that appear constant in a mountains stream or the certain experiments with vibrating strings that we performed in general science as a way of understanding sound.

Instructions Top

Window Size (iterations). [BLUE HIGHLIGHTS].

This is the most important control conceptually because it adjusts the phase relations between basin length and the processing of the basin (and this allows the extraction of different aspects of the dynamic patterns portrayed here.

Drag the Slider (highlighted in blue) from its default setting of 60 down to whatever size is suggested above for using the particular applet you are viewing. In this case the slider has been dragged down to 11 iterations.

Click the Slider Bar. Optionally you may click on the Slider Bar and the Window Size will slowly scroll in the direction (to right of slider or to the left of slider) you want. You can easily get a change of one unit by clicking on the slider bar. This gives you a finer degree of control over window size than does dragging the slider.

Read the Window Size. To the right of the Window Size area is a number (highlighted in blue) that tells you exactly what the Window Size is. Top

Setting Delay. [YELLOW HIGHLIGHTS].

WHY?: Adjusting your Computer's speed to your Monitor's speed: Most monitors cannot paint accurately faster than 66 to 77 times per second. In this class dynamic systems, we ask the computer to paint each iteration of the system to the screen. Depending on the how fast your computer is (it's clock speed mega-Hz or giga-Hz and what type of video card it has) this software may send requests to paint images 1000 or more times per second. Once the iterations per second is higher that 65 or 70 iterations per second (ips) what you see on the screen is some undetermined interaction between your monitor hardware and the behavior of the dynamic system. In other words, you aren't seeing the behavior of the system any more, you are seeing that part of the behavior that the screen happens to capture.

Solution. Click on the Use Speed radio button (highlighted in yellow). Then drag the Delay (between iterations) Slider (highlighted in yellow) from its (very slow) 250 millisecond delay between iterations down to some lower value that gives you a good sense of dynamic motion in the output. As we said, you generally want the the iterations per second (ips) to between 20 ips and 60 ips, although it seems to work well in this case as low as 6 to 8 ips. You your judgment as this is about your perception.

If your computer is slow, you may not need to use the Speed control. Top

Iterations per Second (ips). [HIGHLIGHTED IN LAVENDER].

When you push PLAY, you generally want to have the iterations per second indicator (just to the left of the double black arrow on the control bar) to be between 20 and 60 ips. This range allows you to perceive apparent motion effects but is within your monitor's ability to paint the screen. Obtaining this range may require setting the delay (see below) between iterations.

Perturbing the System. [HIGHLIGHTED IN GREEN].

Perturb Button. Perturbation of a system by changing the states of one or more nodes might (or might not) shift the system to a different basin. The Perturb button will pseudo-randomly change the state of given percentage of nodes. The percentage of nodes perturbed is selected by the user.

Slider. The slider (highlighted in green) allows you to select what percentage from, 0 to 100, of the nodes will have their state changed pseudo-randomly. The exact percentage chosen by the user is indicated (green highlight) to the right of the slider scale.

Note that any unconnected nodes (the top thirty nodes in the image) will pseudo-randomly change their values (white to black or black to white) when the Perturb button is pressed. Because they are unconnected, their changes of value will have not effect on the system. Top

Sizing the Viewing Area. [ORANGE HIGHLIGHTS].

Resize Viewing Area. [ORANGE HIGHLIGHTS]. The dimpled bar between the Controls and the Output Frame (Viewing Area) can be dragged in either direction (as indicated by black arrows). This allows you to adjust the viewing area to see more or less TAO levels.

Full-Interface Viewing Area. [ORANGE HIGHLIGHTS (Top)]. Once you have the controls set as you like them you can eliminate them and see more derivatives by clicking on the little left-pointing arrow at the top of the bar dividing the controls from the output frame. Clicking the right-point arrow will return the controls to view. You can also grab the dividing bar and drag one way are another to size the parts of the interface the way you want.

Pseudo-Randomness. This is a deterministic system and therefore probability is not a concept that applies to its behavior. So it is worth noting that the pseudo-random changes that are part of some functions (e.g., perturb button) are deterministic, although so irregular as to fit human perception of randomness (which is a probability concept).

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