Rössler Attractor

Attractor Builder (Blender add-on)
Equations:
ẋ = - (y + z)
ẏ = x + a*y
ż = b + z*(x - c)
Parameters:
| a = 0.2 | b = 0.2 | c = 5.7 |
Simulation settings:
Initial state: x₀ = 0.01, y₀ = 0, z₀ = 0  
Method: RK4  
Time step (dt): 0.05  
Number of steps: 15000  
Burn-in phase: 1000  
Scale: 0.2

The Rössler attractor was introduced in 1976 by Otto E. Rössler from the Institute for Physical and Theoretical Chemistry, University of Tübingen, Germany. The model was conceived as a simplified analogue of the Lorenz system, aimed at capturing the essence of deterministic nonperiodic flow — continuous chaos — with a single quadratic nonlinearity. Rössler’s goal was to design the simplest possible continuous system that produces a strange attractor while maintaining only one nonlinear term. The original system of equations has the following form (1976, p. 397, Eq. 2):

\(\dot{x}=-(y+z),\quad \dot{y}=x+0.2\,y,\quad \dot{z}=0.2+z\,(x-5.7).\)

It contains only a single nonlinear term, \(z\,x\), making it one of the simplest continuous-time systems exhibiting chaotic behavior. The model was conceived as a "model of a model"—a minimal analog of the Lorenz system that retains the characteristic stretching and folding mechanism responsible for deterministic chaos.

Source:

Rössler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397–398. DOI: 10.1016/0375-9601(76)90101-8