Ternary Density Plot — Matplotlib

A ternary density plot combines a three-component ternary diagram with kernel density estimation to visualize where compositional data concentrates. Instead of showing individual points, this visualization uses a heatmap overlay to reveal the underlying probability distribution of compositions, making it ideal for identifying clusters, modes, and patterns in large compositional datasets.
Ternary Density Plot rendered with Matplotlib
Python source (Matplotlib)

""" anyplot.ai
ternary-density: Ternary Density Plot
Library: matplotlib 3.10.9 | Python 3.13.13
Quality: 92/100 | Updated: 2026-05-19
"""

import os

import matplotlib.pyplot as plt
import numpy as np
from matplotlib.patches import Polygon
from scipy.stats import gaussian_kde


# Theme tokens
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"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"

SQ3H = np.sqrt(3) / 2  # sqrt(3)/2, reused throughout

# Data: sediment composition (sand/silt/clay) with three cluster types
np.random.seed(42)

n1 = 300
sand1 = np.random.beta(5, 2, n1) * 60 + 35
silt1 = np.random.beta(2, 3, n1) * (100 - sand1) * 0.6
clay1 = 100 - sand1 - silt1

n2 = 250
silt2 = np.random.beta(5, 2, n2) * 50 + 40
sand2 = np.random.beta(2, 4, n2) * (100 - silt2) * 0.5
clay2 = 100 - sand2 - silt2

n3 = 250
clay3 = np.random.beta(4, 2, n3) * 45 + 40
sand3 = np.random.beta(2, 5, n3) * (100 - clay3) * 0.4
silt3 = 100 - sand3 - clay3

sand = np.clip(np.concatenate([sand1, sand2, sand3]), 0, 100)
silt = np.clip(np.concatenate([silt1, silt2, silt3]), 0, 100)
clay = np.clip(np.concatenate([clay1, clay2, clay3]), 0, 100)
total = sand + silt + clay
sand, silt, clay = sand / total, silt / total, clay / total

# Ternary → Cartesian: Sand vertex (0,0), Silt vertex (1,0), Clay vertex (0.5, SQ3H)
# x = silt + 0.5 * clay,  y = SQ3H * clay
x_data = silt + 0.5 * clay
y_data = SQ3H * clay

# KDE density grid
grid_res = 200
xi = np.linspace(0, 1, grid_res)
yi = np.linspace(0, SQ3H, grid_res)
Xi, Yi = np.meshgrid(xi, yi)
Ci = Yi / SQ3H
Bi = Xi - 0.5 * Ci
Ai = 1 - Bi - Ci
mask = (Ai >= 0) & (Bi >= 0) & (Ci >= 0)

kde = gaussian_kde(np.vstack([x_data, y_data]), bw_method="silverman")
Z = kde(np.vstack([Xi.ravel(), Yi.ravel()])).reshape(Xi.shape)
Z = np.where(mask, Z, np.nan)

# Plot (12×12 → 3600×3600 px at 300 dpi, valid 1:1 format for symmetric plot)
fig, ax = plt.subplots(figsize=(12, 12), facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)

# Triangle boundary
ax.add_patch(Polygon([[0, 0], [1, 0], [0.5, SQ3H]], fill=False, edgecolor=INK_SOFT, linewidth=2.5, zorder=10))

# Grid lines — three families, one per component (20/40/60/80%)
for lv in [0.2, 0.4, 0.6, 0.8]:
    # Constant Clay% — parallel to bottom Sand–Silt edge
    ax.plot(
        [0.5 * lv, 1 - 0.5 * lv],
        [SQ3H * lv, SQ3H * lv],
        color=INK_MUTED,
        linewidth=0.8,
        alpha=0.35,
        linestyle="--",
        zorder=1,
    )
    # Constant Silt% — parallel to left Sand–Clay edge
    ax.plot(
        [lv, 0.5 + 0.5 * lv], [0, SQ3H * (1 - lv)], color=INK_MUTED, linewidth=0.8, alpha=0.35, linestyle="--", zorder=1
    )
    # Constant Sand% — parallel to right Silt–Clay edge
    ax.plot(
        [0.5 * (1 - lv), 1 - lv],
        [SQ3H * (1 - lv), 0],
        color=INK_MUTED,
        linewidth=0.8,
        alpha=0.35,
        linestyle="--",
        zorder=1,
    )

# Density heatmap and contour lines
density_plot = ax.contourf(Xi, Yi, Z, levels=20, cmap="viridis", alpha=0.85, zorder=2)
ax.contour(Xi, Yi, Z, levels=6, colors="white", linewidths=1.5, alpha=0.6, zorder=3)

# Colorbar
cbar = plt.colorbar(density_plot, ax=ax, shrink=0.65, pad=0.02)
cbar.set_label("Density", fontsize=20, color=INK)
cbar.ax.tick_params(labelsize=16, colors=INK_SOFT)
cbar.ax.yaxis.label.set_color(INK)

# Vertex labels
ax.text(0, -0.06, "Sand", fontsize=22, ha="center", va="top", fontweight="bold", color=INK)
ax.text(1, -0.06, "Silt", fontsize=22, ha="center", va="top", fontweight="bold", color=INK)
ax.text(0.5, SQ3H + 0.05, "Clay", fontsize=22, ha="center", va="bottom", fontweight="bold", color=INK)

# Edge tick labels — each edge shows a DIFFERENT component's % scale
for pct in [20, 40, 60, 80]:
    f = pct / 100
    # Bottom edge: Sand% decreasing left→right (100% at Sand vertex, 0% at Silt vertex)
    # At Sand=f, Silt=1-f, Clay=0 → x = 1-f, y = 0
    ax.text(1 - f, -0.03, f"{pct}", fontsize=13, ha="center", va="top", color=INK_MUTED)
    # Left edge: Clay% increasing bottom→top (0% at Sand vertex, 100% at Clay vertex)
    # At Clay=f, Sand=1-f, Silt=0 → x = 0.5·f, y = SQ3H·f
    ax.text(0.5 * f - 0.04, SQ3H * f, f"{pct}", fontsize=13, ha="right", va="center", color=INK_MUTED)
    # Right edge: Silt% decreasing bottom→top (100% at Silt vertex, 0% at Clay vertex)
    # At Silt=f, Sand=0, Clay=1-f → x = 0.5+0.5·f, y = SQ3H·(1-f)
    ax.text(0.5 + 0.5 * f + 0.04, SQ3H * (1 - f), f"{pct}", fontsize=13, ha="left", va="center", color=INK_MUTED)

# Axis direction labels outside each edge (identify which component the ticks measure)
ax.text(0.5, -0.14, "Sand (%)", fontsize=14, ha="center", va="top", color=INK_SOFT, style="italic")
ax.text(
    0.19, SQ3H * 0.54, "Clay (%)", fontsize=14, ha="center", va="center", color=INK_SOFT, style="italic", rotation=60
)
ax.text(
    0.81, SQ3H * 0.54, "Silt (%)", fontsize=14, ha="center", va="center", color=INK_SOFT, style="italic", rotation=-60
)

# Title
ax.set_title(
    "Sediment Composition Analysis\nternary-density · python · matplotlib · anyplot.ai", fontsize=24, pad=20, color=INK
)

ax.set_xlim(-0.15, 1.2)
ax.set_ylim(-0.22, SQ3H + 0.2)
ax.set_aspect("equal")
ax.axis("off")

plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=300, bbox_inches="tight", facecolor=PAGE_BG)
Part of Ternary Density Plot on anyplot.ai.
Ternary Density Plot — Matplotlib

Python source (Matplotlib)

Other implementations
