# Metanoia:Fractals

Alright I think there is just one more thing I wanna teach you all about, and that’s fractals. Alright going back to evolution. We all understand how that works at this point yeah? So if there was a tree with a golden fruit on it, but only a few people could reach them. They are more likely to get laid than those who cannot. So eventually thru the ages, the offspring will get taller and taller. Simple huh? We’ll that’s evolution, and then we have fractals, the evolution of numbers.

So we all know maths, 1+1=2 and 2+2=4 etc. Real basic stuffs. We’ll that’s maths. Fractals are like what happens when evolution and maths fuck and have babies, you end up with fractals. So Benoit Mandelbrot using his gift to maths (against what his maths teachers told him he was going to become, once again, poking fun at teachers) brought us fractals. So do we all know algebra here? Probably not, but that’s just a variable (it can change) in a formula. E.g. E=MC^{2} Where (E)nergy ↔ variable, (M)ass ← variable. Crashed ya thru maths didn’t I. Oh well that’s not important, so if you don’t follow don’t worry.

So what Mandelbrot thought was that every point on a graph is variable. Did I mention that Mandelbrot worked for IBM (International Business Machines) at this point in his life, and that was when computers were just taking hold in world-wide business I think between the late 60s and early 80s? Because I definitely meant too or else he’d still be sitting there with his abacus figuring out the first fractal.

So I was going to tell you all about the weird equals sign that means a feedback loop and show you all what it looked like, but not even the newest software packages have it included in the font pack. It looks like = but with another line going from the top bar, left of the image, to the top right of the page and another one from the bottom line, right hand side of the image to the bottom left hand corner of the page. So it kinda looks like two arrows firing in opposite direction. I hope I’ve explained it well enough, so that’s the feedback loop sign. Yet for the rest of this book I’m going to be using ↔ instead as it’s almost the same thing.

Alright so you know how to count right? Yeah? 1, 2, 3, 4, 5, 6, 7… and we could continue on for infinity, well that written as a fractal equation is x ↔ x + 1. Amazing isn’t it: all the numbers you can think of can be made by doing that. So let’s say x is equal 1 for the starting point, so therefore 1+1 ↔ 2, therefore 2+1 ↔ 3, therefore 3+1 ↔ 4, and that goes on forever. Pretty simple stuff really huh? This is why I call it the evolution of numbers.

Well what Mandelbrot did was plot onto a graph heaps and heaps of these equations. Like billions of them, for this equation, x ↔ x^{2}+c. What he got at the end of it was a endlessly repeating pattern of awesomeness. It was called ‘the fingerprint of god’ by someone along the lines. So just type that into google or whatever your search engine is. Yet it is officially known as the ‘Mandelbrot Set’. Welcome to the world of fractals. I really wish I could show you it, but no words are going to accurately describe it; but they don’t physically exist, they are just estimates of what’s between two points; I should come back to that hopefully.

So this fingerprint of god is called that because it contains all the ‘structures’ we see before us. Also just to mention, I just ‘liked’ god on Facebook. Go god! So much better than your ‘real’ god, thought I’d throw it in here, and now’s a good a time as ever. So what do I mean structures we see before us? We’ll everything. Everything natural is a fractal. Take the coastline of England as the example (this is because that’s what Benoit Mandelbrot) gave us as the example). Actually, I might go a bit simpler than him and while I talk about this, think about the number Pi (the number involved with anything that involves a circle).

Alright so to get this explained to you, I’ll be talking about the base of my lamp here (lighting lamp), which is a circle. Therefore using this system we’ll also be explaining Pi, and why it is an infinitely long number. Basically because it’s the same thing as my lamp example... and I think this works better than the coast line of England which Benoit Mandelbrot used as an example to describe fractals. Yet I think this way will work a heap better and simpler.

So I don’t know the exact measurements of my lamp here, maybe one of you maths nuts can work it out; but that is not important to the story here. So I am trying to find out the distance around the base of the lamp. The first time I try to figure it out I use a 5cm ruler; but it could just as easily be in inches, the scale of it is not important.

So I measure from point to point using the 5cm ruler and it fits in 7 times. So therefore it is about 35cm around the base. Yet I also notice that I have cut a little bit off by using my 5cm long measuring stick. So I start again but this time I use a 2cm long measuring stick and that goes around 19 times. So therefore it is 38cm around the base. I try again with a 1cm long measuring stick and that gives me 40cm around the base.

This is the way it is, the smaller measurement stick; the longer the measurement is. If you can remember back to when I was asking how long the piece of string? It’s all about the error factor. This fact was a huge problem from early mathematics, until they figured out that Pi is a non-real number. Therefore every equation that uses Pi to figure out a number is ultimately wrong. All it is a rough estimate, a very, very good estimate, but it is only an estimate. So anyways, what Mandelbrot was saying was that the coastline of England could not be measured using conventional mathematics. That is the coastline could only be estimated. No matter how good they got their maps.

This is the part that blew my mind: everything, and I mean everything, in nature is a fractal. Take a tree for instance, what is the formula for a tree? Well take this tree we’re going to build in our minds together, and think about it the next time you find yourself staring at a tree. Alright, so what can you measure? It’s height? It’s age? Both you’ll find a ‘traditional’ answer. Yet what if you want to know more about the tree? How it grows? You could watch it for a really long time, but I don’t have the patience to do that. To tell you the truth, neither do you. Trees don’t grow very fast in human time. So is there anything else about the tree you can tell me?

Well there is something I can tell you and you possibly won’t know this. Yet as everything can be described by mathematics, so can the tree must be mathematics right? We’ll yes it is. If you assume it is a fractal. Let’s say the tree is in 3-2 format. I’ll explain this, from the roots of the tree you have the trunk of the tree and that’s where we’ll start. So the trunk comes up and breaks into three branches, it then goes on and then bam, two more branches. Now each of the branches off the original trunk, breaks apart 3 times, and then 2 times, and then each of the branches coming off those branches will be in the 3-2 fashion. You think I’m joking? Go out and look at a tree, whilst it might not be in 3-2 format, it will be without a doubt, a fractal.

Did I mention why it was called a fractal? ‘cos I don’t really know, well I have learned it in the past, but there’s no way of recalling it I figure it’s gone for good. Good riddance to it too, I don’t need to be filling my mind up with useless information. Yet it has something to do with the fact that it is repetitively fractured. Infinitely fractured... a fractal. Yeah that seems to make sense, let’s go with that.

You ever heard of the chaos theory? Which is ironically why they can’t really predict the weather a week or two in advance. Yes, this is real science. Well the chaos theory goes that the flap of a butterfly’s wings could cause a typhoon half way round the world. Well, that’s pushing it, I don’t think a butterfly is the cause of any typhoon; maybe a collection of butterfly’s who were plotting to cause us catastrophic damage, those evil, evil butterfly’s. Yet I don’t think that’s happened somehow.

So the flapping of a butterfly’s wings pushes air around (so it can fly around and do it’s butterfly things), the air that gets pushed away from the butterfly needs to get replaced by air, so that comes from the opposite side, then that air needs to be replaced… and so on, then before you know it, there’s a hurricane on the other side of the globe.

So the weather is obviously a fractal. Even clouds are fractals: look for it, and you too will see endless repeating structure, or waves, there in there too, there in everything ‘cept manmade shit. This was well noted in art well before it was accepted in science. I still think half of the scientific community won’t know what a fractal is. I’m pretty sure you should all look them up on your interwebs. Pretty frikkin cool. So the chaos theory is a fractal, and so is Pi. Well the math’s that describe them are fractal.

I’m a fractal too, and so are you. Take your hand for instance, the palm of your hand is your body. Your thumb, because it has two parts too it is your neck and your head. Whilst the fingers have three parts on them. So these must be your arms and legs right down to your hands and feet. Don’t believe me, take a look at your foot I’m fairly certain that will be the same.

Fractals man, I’m amazed by them. Also going back to the tree, the odds are that the trees themselves (if naturally planted) will usually follow the same guidelines and the branches. Three in one place, two in the next; for the 3-2 example I just used. The world is fascinating huh? This shit still blows my mind, damn fractals. Thank you Mandelbrot, for this is a valuable insight into the natural world. One that is still largely overlooked and certainly under taught. I never learnt about this shit in school, well we might have done a little bit on the chaos theory, it was never tied to the maths of fractals. Damn you school. Once again, you failed me.

I would have thought that would come in about the time that you learn evolution at school. Come to think about it, I don’t think we were really taught evolution the right way anyways, we come from apes? C’mon guys, we didn’t evolve from apes, we are related to the apes for sure. I just don’t think monkeys would like being called ‘our fathers’. Very unkind to them, I know I wouldn’t want to be the father of siblings who kill themselves. All I’m going to say is that fractal mathematics has changed my view on how mathematics is performed in the natural world. The evolution of numbers, pretty cool aigh? Well I think so. Damn you school for not teaching me about them. I strongly dislike you school, you taught me incorrect shit. Damn you.

To not go on another rant about school, I’m going to peal myself away from fractals now. Yet remember before how I mentioned cat’s paws and them not being fractal, that’s weird as, why they got a different amount of toes on their front paws and back paws I don’t think I’ll ever know. Anyways I think there you have it, enough background information to figure out the meaning of life. Of course I knew these things for years before I realised what it was; and I’m fairly certain there are heaps of people out there that already know this shit but don’t know the meaning of life. Also, I had not figured it out as ‘the meaning of life’, that’s just a side pleasantry of this.

Where almost there people. No more knowledgeable shit is going to come out of this. Just my thoughts, feelings and emotions; and that means shit all. As I said before, I don’t expect the scientific community to accept this is a truth. I’m fairly certain they will figure it out on their own, those damn smart science people. I have utter faith in your results, no faith in my feelings. Also yes, I will provide simple maths I did to prove it to myself. Whilst this maths is just crap, the results are too alike to ignore.

Well I was going to put my two-cents in for war, I think I’ll wait till after I got to the meaning of life for this one. I think that will be really important to know for that little yarn [talk]. I also want to say, that your meaning of life is personal. Your life is your life, and how you choose to live it is your choice. I just feel I got it right as a whole, thinking for everyone.

What do I get for it? Nothing. What do I want to get from it? Nothing. What do I expect from it? Nothing. We’re all just riding the broken wheel of life, so I’m just giving you my perspective of what it is. That is all; and as a species is that not how we develop? So might as well put it out there than take it to the grave with me. Which is highly likely considering I’m a… actually never mind. I’ll come back to it later; but that’s this worlds fault anyways, not mine. We’ll also get to taking the blame for your actions a little later too. Yet I also feel that the meaning of life would help that along.