Friday, September 4, 2009

Math student discovers origin of fractals.

Quantum Black hole. Notice how it is all right triangles making rotating squares. The squares make more and more squares. The definition of a fractal is a shape that when decomposed the pieces are the same or similar to the whole. This and all Jason's fractals are hand drawn.

Breakthrough in Fractal Geometry

This is a quantum sea shell or nautilus. It is one of the most commonly occurring fractals in the universe. Deeply intertwined with and a derivative of the Fibonacci sequence. It's created by the fact that all things in the universe are vibrating as they revolve or spiral around something else. We are on our planet as we revolve around the sun, getting ever so slowly closer to our sun, and are each traveling through points of space time that trace out our own unique path which is always a derivative of the Fibonacci sequence. Tracing out the points of space time that any object is following will always be some sort of spiraling motion or again, a derivative of the Fibonacci sequence. Naturally occurring beauty of 'numbers' in motion. Elegantly simple but becoming infinitely complex through continued motion. The original is hand drawn like all of Jason's fractals. He was the first to discover how to hand draw fractals of anything and is currently the only person worldwide that can hand draw fractals of any shape.

The end of Pi discovered. Pi has relativistic end and is a fractal

In this drawing Jason is showing how perfect circles do not exist...anywhere in the universe. Circles are made from triangles as are all shapes and are deeply interconnected with the number Pi. The more triangles you squeeze within a certain perimeter the closer and closer you approach a circle but you never reach just get closer and closer. This is WHY Pi goes to infinity. Pi is the circumference of a circle (how far around the perimeter) divided by its diameter (the distance from one side of the circle through the center and to the other side). When you add more triangles, the circumference gets slightly larger each time you add more triangles (but by an ever decreasing amount), but the diameter stays the same. A circle with 180 right triangles when you divide it's circumference by it diameter you get 3.141433 (Pi accurate to three decimals). A circle with 360 right triangles, one right triangle every one degree, gives you 3.141552 (Pi accurate to four decimals). This picture is 720 right triangles, which when you divide it's circumference by it's diameter gives you 3.141582 (Pi still accurate to four decimals but almost to five). If we could draw a circle with 25,000 right triangles (and nature does this and far more everyday) it would be 3.141592645 (Pi accurate to seven digits). What is so amazing about Pi is that everything in the universe breaks down into it. All shapes (including circles, and 'perfect circles' don't actually exist..they are made from triangles) break down into straight lines and triangles. Every curve breaks down into microscopic straight lines that change angle by very small amounts (just like this picture looks like a curve but is all perfectly straight lines). In math (trigonometry) they teach how to convert measurements made in degrees (360 degrees is a circle), into measurements made with Pi (this measurement is called Pi radians). To convert degrees into Pi radians you multiply the degrees by Pi/180 (the fraction of pi over 180). All straight lines are 180 degrees (two right triangles make a straight line 90 + 90 =180) and every triangle that exists when you add up all three inner angles always equals 180 degrees (the same as the straight line). Since all shapes that exist break down into straight lines and triangles lets see what happens when we convert the degrees into Pi radians. 180 times Pi/180= 180Pi/180 (in words 180 times pi divided by 180). The 180's cancel out because 180 divided by 180 equals one and one times Pi equals Pi! So every shape in the universe breaks down into pieces of Pi interacting with other pieces of Pi, literally. And some say nature doesn't have a sense of humor! This picture is drawn with straight lines only. It is 720 right triangles rotating 1/2 degree at a time. There is no curve but as you can see the more triangles that are squeezed into the perimeter the more it APPEARS to be a circle or curve. Just like when you look at a mountain and think, that is not a curve or circle, but if you zoom out into outer space and look at the earth it LOOKS like a perfect sphere. But when you're on the earth it looks completely different. In other words, what is a circle is relative. The mountain is not a circle when you're looking at it one the earth, but it looks like a circle (or part of one) from outer space. This is one of the many beautiful illusions of relativity. For those who like the equation aspect, graph f(x)=xsin(Pi/x) and see what happens. As x (the number of sides to a circle) approaches infinity, f(x) will approach Pi. Last but most important is that we have been taught that Pi never ends. That is true when looking at this in pure equation (or mathematical) form...but it is wrong when looking at a 'circle' in reality. This is the really amazing part....Pi ends (physically or more descriptively, in an observational sense). The smallest measurement in the universe is something called a Planck length. The Planck length arises from the limits of observation. In order to observe anything you bounce photons off of it and they bounce back and you observe the geometry of what you are observing. To observe smaller things, you must hit what you are observing with more photons (or more energy) to get a finer reading (or to be able to observe it). As you observe smaller and smaller things you have to hit them with more and more energy to observe them. You eventually reach a physical "limit" to observation. When you try to observe something smaller than a Planck length you must hit it with so much energy that the point that you are trying to observe collapses into a black hole, absorbs the photons and there is nothing left to observe. So while points smaller than the Planck length exist, they CANNOT be observed by us and are therefore not 'RELATIVE'. It was discovered by Maxwell Planck and he won the Nobel prize for it. It's accepted and used worldwide by mathematicians, nuclear physicists etc. What this means is that you cannot physically add an infinite number of triangles in a 'circle'. You can keep adding triangles only until each "side" to the circle (microscopic sides) equals one Planck length and this is where Pi physically (or relativistically) ends without question. The reason mathematicians have missed this (I think) is because of the lack of viewing math from a purely artistic (purely geometric) point of view. When you do equations of circles you never see with your own eyes like you do when you look at this drawing. We are visual creatures and like they say, a picture is worth a thousand words, or in this case, a thousand million equations. One picture shows visually what most would never find in an equation alone.

Currently Pi is calculated as a limit. Mathematicians say that as the number of triangles within the 'circle' approach infinity the value of the circumference divided by the diameter approaches the number Pi.

This is mathematically correct but is incorrect when trying to examine real shapes in the real universe. Pi as a limit is describing a flawless circle. But we know that there is no such thing as a perfect circle because of the Planck constant.

Remember that Pi is a shape (not a number). Numbers only describe geometry (always). So when you use the equation f(x)=xsin(Pi/x), each value of x has one output (numerically) and more importantly, each value of x has one output (geometrically). The input for x always equals the number of 'sides' to the circle. So the output as x changes is always describing a specific shape. When you take into account that each smallest piece of the shape is made of whole multiples pf Planck lengths then you can use this equation to describe every shape that actually exists (relativistically). Whereas Pi as a limit describes nothing that is able to be observed by us and is therefore not relative. If something is not relative (cannot be observed by us in any way) then for all purposes it does not exist relative to us.

Finally, a 'circle' is the ultimate fractal. The definition of a fractal is a shape that when decomposed into pieces is the same or similar to the whole. Every piece of a circle decomposes into a triangle...or Pi.

Where energy comes from discovered. New equation is hf=mc^2

This diagram is pehaps the most important diagram ever drawn. It shows in a simple and elegant way where energy itself (which also means matter) comes from. This shape has been drawn by artists, mathematicans, physicists and others for thousands of years. Some call it sacred geometry, some call it by scientific terms such as grid or lattice. I call it a Planck lattice or .....the structure of space time. This explanation is a little long but the reward is immense if you are interested in knowing where energy (which means matter, which also means you) comes from. Each side to every small equilateral triangle in this diagram represents some thing called a Planck constant or more descriptively a Planck length. A Planck length is the smallest piece or slice of space time that can be observed (or exist relative to us). There is no relative measurement smaller than a Planck constant. Since there are no measurements smaller than a Planck constant then you cannot have a distance that is 1 1/2 Planck lengths because the 1/2 is smaller than the Planck length. This means that when measuring (or observing) slices of space time you can only measure one or whole multiples of one Planck lengths. In other words, any point of space time that exists must be EXACTLY one or whole multiples of one Planck length from all other points. When you try to 'draw' space time you must make all points one or whole mulitples of one Planck length away from all others. This requirement automatically creates the grid like structure of space time. This diagram is the ONLY way that space time can be drawn with whole multiples of Planck lengths. Because there are no fractions the shape that arises is a two dimensional hexagon interacting with other hexagons creating larger and larger hexagons. If you view it three dimensionally you will see that it automatically creates three dimensional cubes that create larger and larger cubes. This is 'why', as Einstein stated, that space time has a grid like structure. This is where that grid structure arises from. Now that we have defined the structure of space time lets look closely at what happens when we 'vibrate' this grid (or Planck lattice) structure. There is something called the Uncertainty principle in physics. What it states is that you cannot locate a particle position and velocity BOTH with perfect precision. What this means is that when you are looking at (or observing) a point of space time it 'vibrates' because you cannot define its position and velocity perfectly. Because of the Uncertainty principle each piece or slice of space time vibrates at the speed of light. This means that every Planck constant (each tiny piece of space time) vibrates at the speed of light. Each Planck constant, in addition to being the same length, has the same (and specific) mass. Now lets see what happens when the structure of space time (or a Planck lattice) vibrates at the speed of light. Look at the center of the diagram and picture it vibrating at the speed of light. Notice that when it vibrates, it vibrates the points connected to it. Also see that the vibrations continue outward and collide with each other head on (at the speed of light) at specific points. (I've drawn little collision points where they collide). This is where the speed of light squared comes from in Einsteins E=MC^2 (in words, energy equals mass times the speed of light squared). Now that we have half of his equation all we need to find is mass. To find the mass all you do is add up the number of Placnk constants (since each have a specific mass) to give you the total amount of mass in a vibrational sequence. So what you have is energy equals the total Planck constants in the vibration (this equals mass) times the speed of light (how fast the Planck vibrate), squared (as the Planck constants collide head on at the speed of light). In reality there are trillions and trillions of collisions occuring at different frequencies which gives rise to all colors, EM waves, gravity, etc. In the diagram I've just drawn collisions at the most common points so it is easier to picture. The equation at the bottom of the diagram describes energy in pure equation form. Maxwell Planck (who discovered and named the Planck constant), won the noble prize in physics and discovered that Energy=hf. In words, energy equals the Planck constant (the 'h' symbol) times frequency (the 'f' symbol). Einstein discovered that Energy=mc^2. In words, energy equals mass times the speed of light squared. Since Energy=hf and Energy=mc^2, then they both equal energy and therefore equal each other. Or, hf=mc^2, in words, the Planck constant times frequency equals mass times the speed of light squared. Combining these two equations and seeing the shape of space time vibrating at the speed of light is the key to understanding where energy comes from. On a final note, notice how the structure of space time is a fractal. (A shape that when taken apart into pieces is the same as the whole). Scientists have know for several years that every shape that exists is a fractal. But they didn't know why. This diagram shows why. Since the structure of space time literally creates all shapes, and space time is itself a fractal, then all shapes that it creates (which is everything) is also a fractal.

Quantum Star (Hand drawn pentagon fractal)

This is a quantum star. It arises from the pure geometry of space time. One pentagon vibratinging in a ripple of water makes this shape always. Whenever you see a five pointed star it arises from a point of space time (in a pentagon form) vibrating all the points connected to it, creating the same shape larger and larger and smaller and smaller. Use the zoom in feature to see the detail in the vectored lines and how it appears to become 3 dimensional. Jason Padgett recently discovered how fractals arise in nature and how to hand drawn a fractal of anything. Currently he is the only person worldwide that can hand draw a fractal of anything. These drawings are more than just beautiful, they are the connection between numbers and physics. They are simple, yet complex, intimidating, yet comforting, empowering and humbling....all at the same time.