def plot_isocontours(ax, func, xlimits=[-2, 2], ylimits=[-4, 2], numticks=101):
x = np.linspace(*xlimits, num=numticks)
y = np.linspace(*ylimits, num=numticks)
X, Y = np.meshgrid(x, y)
zs = func(np.concatenate([np.atleast_2d(X.ravel()), np.atleast_2d(Y.ravel())]).T)
Z = zs.reshape(X.shape)
plt.contour(X, Y, Z)
ax.set_yticks([])
ax.set_xticks([])
def advect(f, vx, vy):
"""Move field f according to x and y velocities (u and v)
using an implicit Euler integrator."""
rows, cols = f.shape
cell_xs, cell_ys = np.meshgrid(np.arange(cols), np.arange(rows))
center_xs = (cell_xs - vx).ravel()
center_ys = (cell_ys - vy).ravel()
# Compute indices of source cells.
left_ix = np.floor(center_ys).astype(np.int)
top_ix = np.floor(center_xs).astype(np.int)
rw = center_ys - left_ix # Relative weight of right-hand cells.
bw = center_xs - top_ix # Relative weight of bottom cells.
left_ix = np.mod(left_ix, rows) # Wrap around edges of simulation.
right_ix = np.mod(left_ix + 1, rows)
top_ix = np.mod(top_ix, cols)
bot_ix = np.mod(top_ix + 1, cols)
# A linearly-weighted sum of the 4 surrounding cells.
flat_f = (1 - rw) * ((1 - bw)*f[left_ix, top_ix] + bw*f[left_ix, bot_ix]) \
+ rw * ((1 - bw)*f[right_ix, top_ix] + bw*f[right_ix, bot_ix])
return np.reshape(flat_f, (rows, cols))
