HD version available here:
01) http://www.youtube.com/watch?v=jlkIxSLRrHU
02) http://www.youtube.com/watch?v=-q2Wj16kTlY
There you have it :) On the left you can see Johan Gielis Superformula doing 1570 rotations. The only parameter used to animate the formula was the 4 in m over 4. But because this is not a variable given in the formula, I added it myself. Instead of just changing the number 4 I introduced a new variable r so that if it is 1, one rotation is achieved (the cartesian coordinates are divided into 4 quadrants, which makes one full rotation when 4 is given.
No extra transformations are needed in order to achieve this animated pattern seen above. The paramaters for the above shape are:
m=1 / n1=0.211 / n2=-0.316 / n3=-0.316 / a=1 / b=1
I decided to stick with one set of parameters and only animate the amount of rotations, given by paramater r, to show the dynamic motion of the formula, which happens to be exactly the same as superflow, a technique I discovered on October 23rd 2009. It is no coincidence that what you see are exact replicas. Not only that, what you see here is the living Rose equation, already discovered in the 18th century.
Superflow can be generated without any mathematical formula. It is a simple procedure, starting out with an object, which is then duplicated any amount of times. All of these objects are then put into a hierarchy, so that the first object is the mother of the 2nd object, which is the mother of the next. After this mother-child hierarchy is setup, the last step is to set the pivot point of each object. The default pivot for each object is the center inside itself, but here lies the secret, which I share with you. Align the pivot for all objects to the center of the mother object. Now that each object rotates around the source, the magic starts to happen.
The first child rotates once around the mother, mother once around itself. The 2nd child rotates two times around the mother, the 3rd child three times, and so on. Each child rotates one more time around the mother than the previous child, creating a superflow, that's what I call it. In this example I used 1570 spheres in order to create the same resolution as the superformula to the left. And if you looked at the trajectory path of each sphere, they are actually only going in circles, all 1570 spheres are just rotating in a circle, but the difference in speed of which each moves, creates these stunning patterns, which can also be found in cymatic sound images.
In order to animate Superflow, I selected all objects and rotated them in the Z-axis 360 degrees. Doing this creates one full rotation for all objects, and each lands right where it started. I duplicated these objects not in a straight line, but so that the beginning position creates one circle, but Superflow is very flexible, and works with any starting position. You can create a superflow with any starting shape. It's a beautiful method and I welcome you to try it out yourself. These two techniques will be studied in my upcoming Bachelor Thesis, for which we are even developing special Particle Software to work in 3D Studio Max, the program I use to create these animations.
These generated geometric patterns are found in nature and in ancient cultures. Superflow, and the Superformula, hold ancient secrets to Life and allow us to have a look into this mystery we are all a part of. You can find the Flower of Life in these patterns, you can find the pentagon star inside every apple you eat, even the Yin and Yang are right here, alive in these patterns. Some call it Sacred Geometry, it is the Geometry of Nature. We live in the Milky Way Galaxy, a huge gigantic spiral. Spirals are everywhere, and they are right here in Superflow and the Superformula. Not only that, nature uses rotational symmetry wherever you look. Most everything has some kind of symmetry, wether it is the energy in the atomic or molecular levels, or the physical body we live in. Rotation is a fundamental force of energy, which Superflow has allowed me to study. Mother-child hierarchies are the essence of Life in nature. That's what it does, it recreates duplicates, which is what we do too. We are all unique and at the same time, we are the same, we all share the same mother. We are all one.
That's all, you can try it in your 3D program of choice today :)
Another interesting fact to note, if you divide the rotation into half, you get 2 folded symmetry (duality, yin yang, infinity sign). Divide 360 by 3, and you get 120degrees, and it shows the thre folded symmetry, trinity. Divide it by 4, and you land at 90degrees and get 4 folded "flowers". Quite amazing I find :)
Hope you enjoy - for more information chek out
http://superformula.mindflow.de
Music:
1) Trois Gymnopedies: No. 1: Lent et douloureux
2) Kim Hiorthoy - Alt måste bli anorlunda
3) 04 - Autechre - Obny overand (overand 333)
