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.
""" anyplot.ai
ternary-density: Ternary Density Plot
Library: bokeh 3.9.0 | Python 3.13.13
Quality: 72/100 | Updated: 2026-05-19
"""
import numpy as np
from bokeh.io import export_png
from bokeh.models import ColorBar, Label, LinearColorMapper
from bokeh.plotting import figure
from scipy.stats import gaussian_kde
# Generate synthetic compositional data (sediment: sand/silt/clay)
np.random.seed(42)
n_points = 500
# Create three clusters of compositions
# Cluster 1: Sandy sediments (high sand)
n1 = 200
sand1 = np.random.beta(5, 2, n1) * 80 + 10
silt1 = np.random.beta(2, 3, n1) * (100 - sand1) * 0.6
clay1 = 100 - sand1 - silt1
# Cluster 2: Silty sediments (high silt)
n2 = 150
silt2 = np.random.beta(5, 2, n2) * 70 + 20
sand2 = np.random.beta(2, 3, n2) * (100 - silt2) * 0.5
clay2 = 100 - sand2 - silt2
# Cluster 3: Clayey sediments (high clay)
n3 = 150
clay3 = np.random.beta(5, 2, n3) * 60 + 30
sand3 = np.random.beta(2, 3, n3) * (100 - clay3) * 0.4
silt3 = 100 - sand3 - clay3
# Combine all clusters
sand = np.concatenate([sand1, sand2, sand3])
silt = np.concatenate([silt1, silt2, silt3])
clay = np.concatenate([clay1, clay2, clay3])
# Normalize to ensure they sum to 100
total = sand + silt + clay
sand = sand / total * 100
silt = silt / total * 100
clay = clay / total * 100
# Convert ternary to Cartesian coordinates
def ternary_to_cartesian(a, b, c):
"""Convert ternary coordinates (a, b, c) to Cartesian (x, y)."""
total = a + b + c
a, b, c = a / total, b / total, c / total
x = 0.5 * (2 * b + c)
y = (np.sqrt(3) / 2) * c
return x, y
# Transform data points
x_data, y_data = ternary_to_cartesian(sand, silt, clay)
# Create density grid
grid_resolution = 200
x_grid = np.linspace(0, 1, grid_resolution)
y_grid = np.linspace(0, np.sqrt(3) / 2, grid_resolution)
xx, yy = np.meshgrid(x_grid, y_grid)
# Create mask for valid ternary region (inside the triangle)
# Triangle vertices: (0, 0), (1, 0), (0.5, sqrt(3)/2)
mask = np.zeros_like(xx, dtype=bool)
for i in range(grid_resolution):
for j in range(grid_resolution):
px, py = xx[i, j], yy[i, j]
# Check if point is inside triangle using barycentric coordinates
# Left edge: y <= sqrt(3) * x
# Right edge: y <= sqrt(3) * (1 - x)
# Bottom edge: y >= 0
if py >= 0 and py <= np.sqrt(3) * px + 1e-6 and py <= np.sqrt(3) * (1 - px) + 1e-6:
mask[i, j] = True
# Compute kernel density estimation
points = np.vstack([x_data, y_data])
kde = gaussian_kde(points, bw_method="scott")
# Evaluate on grid
positions = np.vstack([xx.ravel(), yy.ravel()])
density = kde(positions).reshape(xx.shape)
# Apply mask (set values outside triangle to NaN)
density_masked = np.where(mask, density, np.nan)
# Create figure (4800 x 2700 for landscape format)
p = figure(
width=4800,
height=2700,
title="Sediment Composition · ternary-density · bokeh · pyplots.ai",
x_range=(-0.15, 1.15),
y_range=(-0.12, 1.05),
tools="",
toolbar_location=None,
)
# Remove axes and grid (we'll draw our own ternary grid)
p.xaxis.visible = False
p.yaxis.visible = False
p.xgrid.visible = False
p.ygrid.visible = False
p.outline_line_color = None
# Color mapper for density
color_mapper = LinearColorMapper(
palette="Viridis256", low=np.nanmin(density_masked), high=np.nanmax(density_masked), nan_color="rgba(0, 0, 0, 0)"
)
# Plot density as image
p.image(image=[density_masked], x=0, y=0, dw=1, dh=np.sqrt(3) / 2, color_mapper=color_mapper, alpha=0.85)
# Triangle vertices
tri_x = [0, 1, 0.5, 0]
tri_y = [0, 0, np.sqrt(3) / 2, 0]
# Draw triangle outline
p.line(tri_x, tri_y, line_width=4, line_color="#306998", line_alpha=0.9)
# Draw grid lines inside triangle
grid_alpha = 0.4
grid_width = 2
grid_color = "#306998"
# Draw lines parallel to each edge (10%, 20%, ..., 90%)
for pct in [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]:
# Lines parallel to bottom edge (constant clay %)
y_line = pct * np.sqrt(3) / 2
x_left = pct / 2
x_right = 1 - pct / 2
p.line([x_left, x_right], [y_line, y_line], line_width=grid_width, line_color=grid_color, line_alpha=grid_alpha)
# Lines parallel to left edge (constant silt %)
x_start = pct
y_start = 0
x_end = pct / 2 + 0.5
y_end = (1 - pct) * np.sqrt(3) / 2
p.line([x_start, x_end], [y_start, y_end], line_width=grid_width, line_color=grid_color, line_alpha=grid_alpha)
# Lines parallel to right edge (constant sand %)
x_start = 1 - pct
y_start = 0
x_end = (1 - pct) / 2
y_end = pct * np.sqrt(3) / 2
p.line([x_start, x_end], [y_start, y_end], line_width=grid_width, line_color=grid_color, line_alpha=grid_alpha)
# Add vertex labels
label_font_size = "32pt"
label_offset = 0.08
# Sand (bottom left)
sand_label = Label(
x=0 - label_offset,
y=0 - label_offset / 2,
text="Sand",
text_font_size=label_font_size,
text_color="#306998",
text_font_style="bold",
text_align="center",
)
p.add_layout(sand_label)
# Silt (bottom right)
silt_label = Label(
x=1 + label_offset,
y=0 - label_offset / 2,
text="Silt",
text_font_size=label_font_size,
text_color="#306998",
text_font_style="bold",
text_align="center",
)
p.add_layout(silt_label)
# Clay (top)
clay_label = Label(
x=0.5,
y=np.sqrt(3) / 2 + label_offset,
text="Clay",
text_font_size=label_font_size,
text_color="#306998",
text_font_style="bold",
text_align="center",
)
p.add_layout(clay_label)
# Add percentage labels along edges
tick_font_size = "18pt"
# Bottom edge (Sand percentage, from left to right is 100% to 0%)
for pct in [20, 40, 60, 80]:
x_pos = pct / 100
p.add_layout(
Label(
x=x_pos,
y=-0.05,
text=f"{100 - pct}%",
text_font_size=tick_font_size,
text_color="#666666",
text_align="center",
)
)
# Left edge (Clay percentage, from bottom to top is 0% to 100%)
for pct in [20, 40, 60, 80]:
x_pos = pct / 100 / 2
y_pos = pct / 100 * np.sqrt(3) / 2
p.add_layout(
Label(
x=x_pos - 0.06,
y=y_pos,
text=f"{pct}%",
text_font_size=tick_font_size,
text_color="#666666",
text_align="right",
)
)
# Right edge (Silt percentage)
for pct in [20, 40, 60, 80]:
x_pos = 1 - pct / 100 / 2
y_pos = pct / 100 * np.sqrt(3) / 2
p.add_layout(
Label(
x=x_pos + 0.06,
y=y_pos,
text=f"{pct}%",
text_font_size=tick_font_size,
text_color="#666666",
text_align="left",
)
)
# Add color bar
color_bar = ColorBar(
color_mapper=color_mapper,
width=40,
location=(0, 0),
title="Density",
title_text_font_size="24pt",
major_label_text_font_size="18pt",
title_text_color="#306998",
major_label_text_color="#666666",
title_standoff=15,
margin=20,
)
p.add_layout(color_bar, "right")
# Title styling
p.title.text_font_size = "36pt"
p.title.text_color = "#306998"
p.title.align = "center"
# Save
export_png(p, filename="plot.png")
Part of Ternary Density Plot on anyplot.ai.