Basic Streamline Plot — plotnine

A streamline plot visualizes vector fields using smooth curves that are tangent to the field at every point. Unlike quiver plots that show discrete arrows, streamlines trace continuous paths through the field, revealing flow patterns, circulation, and field topology. This visualization is ideal for understanding fluid dynamics, electromagnetic fields, or gradient fields where the continuous nature of the flow is important.

Basic Streamline Plot rendered with plotnine

Python source (plotnine)

""" anyplot.ai
streamline-basic: Basic Streamline Plot
Library: plotnine 0.15.4 | Python 3.13.13
Quality: 87/100 | Updated: 2026-05-14
"""

import os

import numpy as np
import pandas as pd
from plotnine import (
    aes,
    coord_fixed,
    element_line,
    element_rect,
    element_text,
    geom_path,
    geom_point,
    ggplot,
    labs,
    scale_color_cmap,
    theme,
    theme_minimal,
)
from scipy.integrate import solve_ivp
from scipy.interpolate import RegularGridInterpolator


THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
BRAND = "#009E73"

np.random.seed(42)

nx, ny = 40, 40
x = np.linspace(-3, 3, nx)
y = np.linspace(-3, 3, ny)
X, Y = np.meshgrid(x, y)

U = -Y
V = X

u_interp = RegularGridInterpolator((y, x), U, bounds_error=False, fill_value=0)
v_interp = RegularGridInterpolator((y, x), V, bounds_error=False, fill_value=0)

streamlines_data = []
arrow_data = []
streamline_id = 0

start_points = []

for sx in np.linspace(-2.8, -1.5, 4):
    for sy in np.linspace(-2.5, 2.5, 6):
        start_points.append((sx, sy))

for r in [0.6, 1.3, 2.2]:
    for angle in np.linspace(0, 2 * np.pi, 6, endpoint=False):
        start_points.append((r * np.cos(angle), r * np.sin(angle)))

for x0, y0 in start_points:
    try:
        result = solve_ivp(
            lambda t, pos: [u_interp([pos[1], pos[0]])[0], v_interp([pos[1], pos[0]])[0]],
            [0, 4],
            [x0, y0],
            max_step=0.05,
            dense_output=True,
        )
        if result.success and len(result.t) > 2:
            t_eval = np.linspace(0, result.t[-1], 100)
            trajectory = result.sol(t_eval)

            for j in range(len(t_eval)):
                px, py = trajectory[0, j], trajectory[1, j]
                if -3 <= px <= 3 and -3 <= py <= 3:
                    speed = np.sqrt(px**2 + py**2)
                    streamlines_data.append({"x": px, "y": py, "streamline": streamline_id, "order": j, "speed": speed})

            arrow_idx = int(len(t_eval) * 0.6)
            if arrow_idx < len(t_eval):
                ax, ay = trajectory[0, arrow_idx], trajectory[1, arrow_idx]
                if -3 <= ax <= 3 and -3 <= ay <= 3:
                    arrow_speed = np.sqrt(ax**2 + ay**2)
                    arrow_data.append({"x": ax, "y": ay, "speed": arrow_speed})

            streamline_id += 1
    except Exception:
        pass

df = pd.DataFrame(streamlines_data)
df_arrows = pd.DataFrame(arrow_data)

anyplot_theme = theme(
    plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
    panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
    panel_grid_major=element_line(color=INK, size=0.3, alpha=0.10),
    panel_grid_minor=element_line(color=INK, size=0.2, alpha=0.05),
    axis_title=element_text(size=20, color=INK),
    axis_text=element_text(size=16, color=INK_SOFT),
    plot_title=element_text(size=24, color=INK),
    legend_text=element_text(size=16, color=INK_SOFT),
    legend_title=element_text(size=18, color=INK),
    figure_size=(16, 9),
)

plot = (
    ggplot(df, aes(x="x", y="y", group="streamline", color="speed"))
    + geom_path(size=1.2, alpha=0.8)
    + geom_point(
        data=df_arrows,
        mapping=aes(x="x", y="y", color="speed"),
        shape=">",
        size=4,
        inherit_aes=False,
        show_legend=False,
    )
    + scale_color_cmap(cmap_name="viridis", name="Flow Speed")
    + labs(x="X Position", y="Y Position", title="streamline-basic · plotnine · anyplot.ai")
    + coord_fixed(ratio=1)
    + theme_minimal()
    + anyplot_theme
)

plot.save(f"plot-{THEME}.png", dpi=300, verbose=False)

Part of Basic Streamline Plot on anyplot.ai.

Other implementations