I recently made some experiments in programming strange attractors, and I found this (very simple) equations, which create a nice strange attractor:

```
xn=x+dt*(z-y)
yn=y+dt*(x/2-1)
zn=z+dt*(-xy/2-z)
```

You can see it in action on my Youtube channel: https://youtu.be/Bm_M6mUGjtg

My question: Is this a variation of the Lorenz- or Rössler attractor - or did I stumble upon something new?

**EDIT:**

Meanwhile I programmed a little 3D View for this attractor:

You can see/move the view on this applet (Java needed): https://cerumen.de.cool/attractor/index.html (Here you also find the source code for Processing)

And here the Javascript-Version: https://cerumen.de.cool/attractor/js/index.html (with processing.js... bit slow)

Perhaps my question was also asked too amateurishly. I was simply surprised by the simplicity of the system of equations I have found.

Therefore I would like to know if this strange attractor is a descendant of one of the well known ones (Lorenz / Rössler).

**Edit 2:**

I have now brought the system of equations into a more general form:

```
xn=x+dt*(z-y)
yn=y+dt*(ax-b)
zn=z+dt*(-axy-z)
```

with a in range [0 to 1], b in range [0.5 to 1]

This makes it more interesting. Here some sample images for different values for a and b:

**Edit 3:**

Here a video with the generalized equations and constantly changing parameters a and b: https://youtu.be/gxusM8pmNwU

I think you can see here quite well how the system goes from order through bifurcation into chaos...

veryclose to the Rossler system: two coordinates with linear differential equations, one 'slightly' nonlinear one, with a quadratic perturbation term. While the specific form of the linear piece is slightly different, I wouldn't be surprised if the two are fundamentally equivalent in some fashion. $\endgroup$ – Steven Stadnicki Feb 18 at 20:29isa particularly nice one and you've made some great pictures of it, but it's not really very novel. $\endgroup$ – Jim Belk Feb 19 at 11:42anothernew strange attractor. But I still love the simplicity of the equation system, which really surprised me when I programmed this thing. $\endgroup$ – klangforscher Feb 19 at 12:42