Rössler Attractor

Rössler Attractor

The Rössler system (1976) is a set of three ordinary differential equations that produce one of the simplest examples of a strange attractor in 3D:

$\dot{x} = -y - z, \quad \dot{y} = x + a y, \quad \dot{z} = b + z(x - c)$

With the classic parameters a = 0.2, b = 0.2, c = 5.7, the system exhibits chaotic behaviour. The attractor looks like a band that folds back on itself — the folding mechanism is a key intuition for how chaos arises in continuous systems.

Integration via the Euler method (x_{n+1} = x_n + dt · ẋ_n) is the simplest numerical approach. While not the most accurate, it captures the qualitative chaotic dynamics for small enough step sizes.

Implement the following functions:

• rossler_deriv(x, y, z, a, b, c) — compute the derivatives (ẋ, ẏ, ż) of the Rössler system
• rossler_euler(x0, y0, z0, a, b, c, dt, steps) — integrate using Euler's method for steps steps, returning the final (x, y, z)