Basic Streamline Plot — lets-plot

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 lets-plot

Python source (lets-plot)

""" anyplot.ai
streamline-basic: Basic Streamline Plot
Library: letsplot 4.9.0 | Python 3.13.13
Quality: 93/100 | Updated: 2026-05-14
"""

import os

import numpy as np
import pandas as pd
from lets_plot import (
    LetsPlot,
    aes,
    element_line,
    element_rect,
    element_text,
    geom_path,
    ggplot,
    ggsize,
    labs,
    scale_color_gradient,
    theme,
    theme_minimal,
)
from lets_plot.export import ggsave
from scipy.integrate import solve_ivp


LetsPlot.setup_html()

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"

# Data - Create a vortex flow field: u = -y, v = x (circular streamlines)
np.random.seed(42)

x_min, x_max = -3, 3
y_min, y_max = -3, 3

# Seed points for streamlines - distributed radially for good coverage
radii = np.linspace(0.3, 2.8, 8)
seed_points = [[r, 0.0] for r in radii]

# Integrate streamlines forward
streamline_data = []
streamline_id = 0

for seed in seed_points:
    t_span = [0, 2 * np.pi]
    t_eval = np.linspace(0, 2 * np.pi, 100)

    # Inline velocity field calculation: rotation field u=-y, v=x
    def velocity_field(t, point):
        x, y = point
        return [-y, x]

    try:
        sol = solve_ivp(velocity_field, t_span, seed, t_eval=t_eval, method="RK45", dense_output=True, max_step=0.1)

        if sol.success:
            xs = sol.y[0]
            ys = sol.y[1]

            mask = (xs >= x_min) & (xs <= x_max) & (ys >= y_min) & (ys <= y_max)

            if np.any(mask):
                xs_clipped = xs[mask]
                ys_clipped = ys[mask]
                magnitudes = np.sqrt(xs_clipped**2 + ys_clipped**2)

                for i in range(len(xs_clipped)):
                    streamline_data.append(
                        {
                            "x": xs_clipped[i],
                            "y": ys_clipped[i],
                            "magnitude": magnitudes[i],
                            "streamline": streamline_id,
                        }
                    )
                streamline_id += 1
    except Exception:
        continue

df = pd.DataFrame(streamline_data)

# Plot
plot = (
    ggplot(df, aes(x="x", y="y", group="streamline", color="magnitude"))
    + geom_path(size=1.5, alpha=0.85)
    + scale_color_gradient(low="#306998", high="#FFD43B", name="Field Strength")
    + labs(x="X Position", y="Y Position", title="streamline-basic · letsplot · anyplot.ai")
    + ggsize(1600, 900)
    + theme_minimal()
    + theme(
        plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
        panel_background=element_rect(fill=PAGE_BG),
        panel_grid_major=element_line(color=INK_SOFT, size=0.3),
        axis_text=element_text(size=16, color=INK_SOFT),
        axis_title=element_text(size=20, color=INK),
        plot_title=element_text(size=24, color=INK),
        legend_title=element_text(size=18, color=INK),
        legend_text=element_text(size=14, color=INK_SOFT),
    )
)

# Save PNG (scale 3x to get 4800 x 2700 px)
ggsave(plot, filename=f"plot-{THEME}.png", path=".", scale=3)

# Save HTML for interactive version
ggsave(plot, filename=f"plot-{THEME}.html", path=".")

Part of Basic Streamline Plot on anyplot.ai.

Basic Streamline Plot — lets-plot

Python source (lets-plot)

Other implementations