Algodoo

This is a thing I always wanted to do. The Lorenz Attractor is a so called differential equation existing in the 3rd Dimension. Differential equations are formulas where you dont calculate the position of the point depending on another coordinate, but the movement change itself. In this case the equation would be:
x' = 10*(y-x)
y' = x*(28-z)-y
z' = x*y-2.666*z
To visualize this, one would have to place a point somewhere in the coordinate system, and then keep applying the function depending on the points position.
This creates a streamlike effect, pushing the point through the coordinate system, with the same position always applying the same "stream". In this scene the Lorenz attractor is drawn by a point starting at x=0.01 since the point x=0 y=0 z=0 would completely freeze the drawer. It is possible to change the 3 values 10 28 and 2.666 (The Lorenz coefficients) to create different patterns, or change the function itself (dx = ***, dy=...) in order to experiment with different patterns.
Note that all Patterns are placed in a 3D coordinate system, so seemingly intersecting lines are always in different depth(Since lines can hardly intersect here since the intersection point would push both lines in the same direction, efficiently fusing them).

About this attractor itself:
The Lorenz attractor is called a strange attractor since all points in the entire space, from infinity to infinity, will end up in the center area, basically "attracting" them to it (reason for being an attractor). At the same time, these points follow fractal or chaotic patterns i.e. never really matching up over time(reason for being a strange attractor). The attractor itself takes the shape of 2 circular disks positioned in a V shape. All points home onto these 2 disks, and after reaching them, continue spiraling outwards along the disk. At a certain radius from the center of the disks, the points will stop orbitting it and instead derail from it at the end of the orbit, continuing towards the other disk. Upon hitting it, they quickly align and continue spiraling outwards until the process repeats. The special property of this equation is that a minimal change in the coordinates of the starting point will end up with completely different results after a certain time. 10 points that only differ by .0001 in the x coordinate each would first all run along the same line, but delayed from each other. However, after a few orbits, the points suddendly spread out and get stretched between both disks. A further orbit results in the group seperating, with some points still orbitting the first disk, and some orbitting the second one. If one continues the process, the points will effectively mix up completely and will be distributed evenly across both disks.

Thingy you may change for experimenting with the formulas:
_a, _b, _c as constants in the equations.
_x, _y, _z as starting point of the Point.
_rotx, _roty, _rotz as angles to rotate the entire image in degrees.
dx=, dy=, dz= as the differential equations.

Please remember to only change these values at the start of the scene, before anything is drawn.
I hope you will enjoy this yet another mathematical image.