The 'Equations of Life'

[route89]

Well, this is my first post, so hello to everyone and here's something for you to think about. I recently watched a documentary called 'The Colors of Infinity' (

) by Arthur C. Clarke, the brilliant visionary scientist and author of '2001: A Space Odyssey'. In this documentary, he suggests that there may be some correlation between fractal geometry and the fundamental biological processes that create life in the real world. He compares the spirals seen in many fractals to the spirals seen in fern leaves and seashells, as well as many other similarities between fractal images and organic structures. He also notes that the infinite variety of endlessly complex fractal images are all created by repeating very simple equations, which is similar to the way that very complex living organisms are also created by repeating one single action, the process of cell division, over and over again until a complete, living organism is created.

 

The idea is that there must be some set of physical rules, or mathematical equations, that determine the position that each cell takes in relation to all the other cells as any living organism is being formed. Otherwise, we would all be formless, non-functioning blobs of tissue. Whether you believe that DNA or God guides the cells into forming a living being, you can still describe the process mathematically using a series of simple equations that break down the angles, movements, weight, positioning, electrical charges, size, etc of the cells as they arrange themselves in exactly the right way to end up with a living, breathing organism. These could be called the 'Equations of Life'.

 

Now, I've been a computer programmer for over 20 years, and in my 4th semester of Calculus I wrote a very simple program that creates an image of the famous 'Mandelbrot Set'. So, after watching Arthur C. Clarke's documentary I started tinkering with my program to see if I could modify it to produce some patterns that resemble organic structures, like the ones in his documentary. After countless hours of modifying my program with little or no significant results, I happened to add one simple modification (only 8 keystrokes) to the equations I'm using, and when I ran the program again, instead of the familiar pear-shaped image of the Mandelbrot Set, this is the image that it produced:

It's hard to express just how baffling this image is to me. I have a degree in Math, and from a mathematical perspective this is borderline impossible. And yet, there it is. A complete, detailed image of a fish made up entirely of Mandelbrot points. I want to stress that I did not start with an existing image of any kind and alter it with Photoshop or any other graphics program of any kind in any way. It was produced, dot by dot, exactly as you see it, exactly the same way the Mandelbrot Set is produced, using the exact same equations that produce the Mandelbrot Set plus one simple modification I added to the original equations.

 

I have since made some refinements to the numerical ranges and precision of the values I'm plugging into the variables I'm using, and I also made some changes in the color gradients for cosmetic enhancements. The equations themselves and the modification I made to them are exactly the same. Here are some closeup images that were created:

There actually appears to be outlines of scales, muscle tissue, and even nerves or blood vessels in these images, all produced by the same program and the same equations. So how can this possibly happen? What does this mean? Is it possible that the equations in my program are the 'Equations of Life'? What other explanation is there? How could this possibly be just a coincidence?

 

So that's it. Strange, but true. At this point I guess I'd like some suggestions about what to do next. Maybe I could submit a CD to the administrator - no viruses, no adware, just one very small program. Then, if he OK's it, I'd be willing to send anyone that's interested a copy of the exact program, and the exact equations, that produce all of the images you see here, and many more. But, if it turns out that this actually is some kind of amazing discovery, I'd like to get some credit for it. I can't just give it away. Can anyone tell me how to do this? It would be a shame for this program to just fade away without at least some research into whether there's some valid, important Science here.

 

In the end, I'm not claiming to be some genius that just discovered the secret of life, and this is not an argument for or against intelligent design or evolution or anything. It seems like I just happened to know enough about programming, math, the Mandelbrot Set, biology, and Arthur C. Clarke to have come up with something that is, at the very least, a very, very strange connection between the equations that produce fractal images and the image of a living organism. Wouldn't it be something if the same equations that produce the infinite beauty of fractal images are somehow related to the wondrous process that produces the endless variety of living organisms in the real world? THANKS!

 

- Scott Hasbrouck EMAIL REMOVED

Edited May 31, 2009 by Klaynos
removed email addy

[Mokele]

Ok, there are aspects of this post that are right, and aspects that are wrong.

 

Firstly, yes, there is a level of mathematical logic behind organism forms, and in some cases, a level of 'recursion' which can yield fractal-like forms, particularly in the forms of plants and flowers, which tend to have relatively simple, repeated developmental programs.

 

However, the "fish" is, at best, illusory.

 

You see a fish because your mind is specifically programmed to find patterns - the same reason many optical illusions work.

 

The outlines of scales, muscles, nerves, blood vessels all do not exist (a dead giveaway is that your 'fish' is symmetrical about the horizontal axis, while real fish are highly asymmetrical about this axis, especially internally). I've dissected a fair few fish in my day, and can assure you that nothing in that picture actually resembles the true anatomy of a fish. The pectoral and pelvic fins are entirely absent, the tail shows a diphycercal morphology seen only in lobe-fin fish, the gills and complexities of the skull are missing, and there is a large amount of extraneous 'stuff' around the posterior end of the "fish". Actual musculature of fish bears at best a superficial resemblance to your image, and your nerves and blood vessels do not correspond to any anatomical locations.

 

So, sorry to disappoint, but it's really nothing more than a pattern that your brain has forced to fit into the 'fish' shape. A 90 degree rotation makes it a fountain or a mushroom just as convincingly. It doesn't really tell us anything about fish, or biology as a whole.

[route89]

I appreciate your comments, and I actually agree with everything you've said. However, it seems to be asking a lot to expect 4 simple equations in a computer program to produce an exact duplicate of a living organism. And I also have to say that this seems like more than my mind being programmed or forced to find a pattern that looks like a fish. It's instantly recognizable as a fish, an Angelfish to be specific, which is fairly close to being symetrical. I've rotated these images, and they don't look like mushrooms or fountains, they look like fish turned on their side.

 

In the real world, there are outside environmental conditions present during an organism's creation that influence the final appearance that organism. If I modified my program to mimic these actions by slightly changing the numerical values that I plug into the variables during the computer's 'creation' process, the images produced would also be slightly different. I could certainly produce asymetrical images by doing this, and maybe even add a fin, but to expect an exact duplicate is not realistic. There is a difference between mathematical simulations and the real world. There are too many variables in the real world to ever produce a perfect mathematical simulation. There isn't even such a thing as a 2 by 4 in the real world, it's always + or - some tiny fraction of an inch. We use Pi all the time in the real world, even though in the world of Math the exact value of Pi will never be known. The square root of -1 does not exist in the real world, but in Math, and in my program, it's used all the time.

 

My point is that it seems premature to dismiss this program I've written because it doesn't instantly produce the exact results you're expecting, and to disregard any possibility of new science without making at least a token effort to explain why these images look so much like a fish even though they are produced entirely by the same 4 simple equations that produce images of the mysterious Mandelbrot Set. And just to complicate things a little more, I just modified my own modification in the program, and I'm now getting images like this:

[Klaynos]

I think the answer might be simply because the human eye/brain is very good at looking for and finding patterns....

[ydoaPs]

I think the answer might be simply because the human eye/brain is very good at looking for and finding patterns....

 

In fact, that's how the brain works. At least the neocortex; it's a pattern finding/comparing machine.

[Mokele]

It only looks like a fish to you because you first saw it as a fish. Re-write the program so it shows these equations flipped 90 degrees, show them to other people, and I guarantee they'll see different things from you.

 

It's nothing more than a sophisticated Rorschach (inkblot) test. Show someone a symmetrical image, and they'll find something it looks like. That you can come up with images that look like animals is basically irrelevant, testifying to little more than the inventiveness of the human mind and the prevalence of bilateral symmetry in animals.

 

 

There's a few serious questions that need to be addressed here:

 

1) Why, prior to even running the program, would you expect there to be any resemblance?

 

2) Why would this have any great insight, considering that actual fractal patterns in nature are the exception, not the rule. Most organisms display *no* level of fractal organization.

 

3) Is there any underlying basis to numbers/variables that you claim produce "animal-like" shapes? Or are you just running numbers until the shapes look right?

 

4) What about numbers/variables that don't give you the desired results?

 

5) Is it even possible to produce a pattern that doesn't look like some animal somewhere, especially considering the vast diversity of past and present shapes?

 

6) How similar does a shape have to be in order to be consider "resembling" a given animal?

 

7) If you're considering even broad similarities as meaningful, how do you distinguish between similar animals (ie a snake vs a worm vs an eel vs a blade of grass).

 

8) What is your basis for discarding IDs are fungi or plants?

 

9) Does the whole organism have to be present, or do you accept 'organs', such a flowers or fruit?

 

 

 

However, most important by far:

 

10) The CORE of the scientific method is falsification of hypotheses. Every scientific theory must have criteria which will invalidate them if found to be true. What are your criteria?

 

11) The primary application of the scientific method is testing hypotheses, often against competing hypotheses. How would you test your hypothesis (that these fractals are somehow informative) against mine (that they're the human mind applying patterns to random symmetrical images). My hypothesis predicts that a viewer would be able to find *something* in the natural world for *any* fractal, and would additionally be able to do so for any bilaterally symmetric inkblot, but that this would fair when the constraint of symmetry was removed. What is your prediction, and how would you test it?

 

 

Remember 10 & 11 are science. All of it. Anything which cannot answer those is not science.

 

 

Also, lest you think I'm being too harsh, this is how science works. I've gotten and given reviews far harsher than this on legitimate scientific papers that had solid backing and no serious methodological flaws. It's a harsh world, and you have to be prepared to have every aspect of your work scrutinized in microscopic detail.

[MM6]

Sorry route89, but I have to agree Mokele, this seems like an example of pareidolia. Your image resembling an angel fish does resemble it in a vague way. It also looks like a tree. There are so many different biological forms that your bound to have an image that looks like something. I don't see that as being useful. The blob that you have paired next to the horseshoe crab is really reaching.

 

A more convincing argument could be made if there was a strong relationship between the inputs of your equation and the cladistic relationship of the output images/"organisms." For example, with a cluster of inputs that yield "crustacean-like" images, a relatively small shift in the input values in one direction would produce hexapods, while a shift in the other would produce myriapods.

 

Now that I'm thinking more about it, this would be misleading too, as morphology is not a strong predictor of evolutionary history/relatedness (and consequently pattern development). I don't see how your program predicts anything relevant in organismal pattern development because of it's sole focus on morphological similarities.

[route89]

Oh well, I guess it doesn't look like a fish or a horseshoe crab. Thanks for the comments.