- #1

- 654

- 148

This attractor is unusual because it uses both the tanh() and abs() functions. A picture can be found here (penultimate image). Here is some dependency-free Python (abridged from the GitHub code, but not flattened!) to generate the data to arbitrary order:

To run it

Enjoy!

[EDIT] fixed bug in t_abs() !

Python:

```
#!/usr/bin/env python3
from sys import argv
from math import tanh
def t_jet(n, value=0.0):
jet = [0.0] * n
jet[0] = value
return jet
def t_abs(u, k):
if k == 0:
return abs(u[0])
elif k == 1:
return u[1] if u[0] > 0.0 else (-u[1] if u[0] < 0.0 else 0.0)
return 0.0
def t_prod(u, v, k):
return sum(u[j] * v[k - j] for j in range(k + 1))
def t_tanh_sech2(t, s2, u, k):
if k == 0:
return tanh(u[0]), 1.0 - tanh(u[0])**2
tk = s2[0] * u[k] + sum(j * u[j] * s2[k - j] for j in range(1, k)) / k
return tk, - (2.0 * (t[0] * tk + sum(j * t[j] * t[k - j] for j in range(1, k)) / k))
def main():
model, order, δt, n_steps = argv[1], int(argv[3]), float(argv[4]), int(argv[5]) # integrator controls
x0, y0, z0 = float(argv[6]), float(argv[7]), float(argv[8]) # initial values
x, y, z = t_jet(order + 1), t_jet(order + 1), t_jet(order + 1) # coordinate jets
if model == "wimol-banlue":
a_ = t_jet(order, float(argv[9])) # constant jet
tx, sx = t_jet(order), t_jet(order) # temporary jets
print(f'{x0:.9e} {y0:.9e} {z0:.9e} {0.0:.5e}')
for step in range(1, n_steps + 1):
x[0], y[0], z[0] = x0, y0, z0 # Taylor Series Method
for k in range(order):
tx[k], sx[k] = t_tanh_sech2(tx, sx, x, k) # sech^2 stored but not used in ODE equations
x[k + 1] = (y[k] - x[k]) / (k + 1)
y[k + 1] = - t_prod(z, tx, k) / (k + 1)
z[k + 1] = (- a_[k] + t_prod(x, y, k) + t_abs(y, k)) / (k + 1)
x0, y0, z0 = x[order], y[order], z[order] # Horner's method
for i in range(order - 1, -1, -1):
x0 = x0 * δt + x[i]
y0 = y0 * δt + y[i]
z0 = z0 * δt + z[i]
print(f'{x0:.9e} {y0:.9e} {z0:.9e} {step * δt:.5e}')
main()
```

Code:

`./wb.py wimol-banlue 16 10 0.1 10001 1 0 0 2.0`

[EDIT] fixed bug in t_abs() !

Last edited: