Logistic Map
A logistic map simulation that iterates x_{n+1}=r*x_n*(1-x_n) to illustrate chaos.
Level:Advanced
Dynamic Behavior Patterns
Explore common system behaviors: exponential growth, goal-seeking decay, overshoot-and-collapse, and S-curve saturation.
Explore Dynamic Behavior Patternssimulation.py
Exploring chaos with the logistic map
The logistic map follows the rule x_{n+1} = r * x_n * (1 - x_n). As we crank up the growth rate r the behaviour shifts from calm equilibrium, through period doubling, and eventually into chaos. Try a value near 3.5 to watch the system go wild.
from tys import probe, progress
Run the logistic map simulation.
def simulate(cfg: dict):
import simpy
env = simpy.Environment()
r = cfg["growth_rate"]
x = cfg["initial_value"]
steps = cfg["steps"]
done = env.event()
Iterate the map for the configured number of steps.
def iterate():
nonlocal x
for i in range(steps):
x = r * x * (1 - x)
probe("x", env.now, x)
yield env.timeout(1)
progress(100)
done.succeed({"final_x": x})
env.process(iterate())
env.run(until=done)
return done.value
def requirements():
return {
"builtin": ["micropip", "pyyaml"],
"external": ["simpy==4.1.1"],
}
Default.yaml
initial_value: 0.4
growth_rate: 3.7
steps: 50
Charts (Default)
Final Results (Default)
| Metric | Value |
|---|---|
| final_x | 0.72 |
FAQ
- How does the simulation produce chaotic behavior?
- Iterating x = r * x * (1 - x) for high r values like 3.5 leads to period doubling and chaos.
- How is the map iterated in SimPy?
- The iterate process updates x and yields env.timeout(1) each step so time advances discretely.
- What does the x probe capture?
- It records the value after each iteration to show bifurcations over time.