Jafar's Math Curriculum Proposal to the Sixth Slawkenberg Council on Education

Jafar's Beginner's Guide To The Chaos Game

A Young Slawkenberger's Introduction to our Wonderous Fractal Universe

So, young Slawkenberg Student! You wish to walk the path of the Changer of Ways? You wish to ride the tides of Chaos, to see the crackling beauty of the fractal Empyrian?

Know this: the Architect of Fate is a God of of hidden order- a God of unseen rules of breathaking simplicity and power that grow forth into astonishing complexity and apparent chaos.

Know the rules, and see the vast and hidden workings of the Architect! First, you see what is hidden. Then, you call forth what is unseen, and revel in the hidden rules of the Emperyon! Once you understand the game, you may become a writer of rules, a caster of spells, an Architect of your own Fate in the wonderful, whirling chaos of Destiny.

But one must crawl before one can walk. One must walk before one can run. And one must run before one can take flight.

Join me, in exploring your first step into the hidden, ordered chaos of the changer of Ways.

As befits all students who are taking their first steps along the paths of power, we begin with a simple practice piece. Let us observe how a few simple rules can create the appearance of great complexity.

Legend tells of an ancient, wartime sage from the mists of Terra, from before the Corpse God ever ruled, and far before he fell. Humans were wise even then, and of the wise, there was a sage named Serpinski.

He created the trangle that, for millenia, has born his name.

Observe how, as an object, it looks both astonishingly simple, and infinitely complex.

It is obvious that this object has rules. Let us examine what those rules are, shall we?

First, let us observe the rules in motion, as we must observe the laws and rules of change in our own day-to-day lives.

Every scribe is familiar with both the tedium of copying, and the power of having multiple copies.

Contemplation of this Serpinski's triangle, this Tzeenchian Toy, is a proper practice piece for those who aspire to fuller comprehension of the underlying, unifying order behind Chaos.

As children, we must crawl before we walk. Let us crawl through our first steps into a wider understanding of Chaos.

This method of understanding Chaos, as befits our origins in the stultifying Imperium, is extremely organized, very systematic, and slow.

But, as our dear Liberator is wont to say, we must build with the foundations we have: and our foundations are Imperial.

Fear not. This organized system is but the first, slow step to the completely disorganized, fundamentally random, yet still regulated and extremely fast Chaos Game.

But for the nonce, we must copy. And so we create Serpinski's Triangle with the Multiple Reduction Copy Machine method.

When operating a copy machine, it helps to have something to copy. Above, I'm making a tzeenchian rune on a white background so that I have something to copy.

In the above, I am running the original drawing through a copy machine. That copy machine shrinks the image down by half and moves it to the lower left corner of the white square. This shrinking and moving is called a transformation. As we hope to be transformed by the Lord of Change, so this squiggle is transformed.

Since this is the multiple reduction copy machine method, it's time to use the second copy machine. This one makes a copy of the original drawing, shrinks it, and place is it in the upper left hand corner of my square.

With this multiple reduction copy machine method, I have taken my original drawing and run it through three reduction copy machines. I am left with three smaller copies of my original drawing arranged in a triangle.

We have created three smaller copies, and deleted the original.

So are multiple reduction copy machine has created three copies and deleted the original. These three copies form a new image. What if we took that new image and ran it through the multiple reduction copy machine again? And again? And again?

This creates a fractal called Serpinski's Triangle.

The amazing thing is that you can start out with any image. Yet, following those three simple rules...you always end up with the Serpinski's triangle.

By adherance to three simple copying rules, we have created a very complex triangle.

This method illustrates the strength of the Imperium: simple, organzied, creating complexty by strict adherence to a heirarchy, sequence, and to the rules.

It has one besetting, overarching sin.

It is slow.

Next, I shall teach you how to make exactly the same result, without heirarchy. Without sequence. Utterly disobedient to, yet...achieving exactly the same result...in a fraction of the time.

Next, I shall teach you...the Chaos Game!