A log-log scatter plot comparing two material properties (e.g., Young's modulus vs. density) with material families displayed as labeled bubble regions. Developed by Michael Ashby for systematic material selection in engineering design, this chart enables rapid visual comparison of material classes across multiple property dimensions. It is a standard tool in materials science and mechanical engineering education.
""" anyplot.ai
scatter-ashby-material: Ashby Material Selection Chart
Library: matplotlib 3.10.9 | Python 3.13.13
Quality: 91/100 | Updated: 2026-06-03
"""
import os
import matplotlib.patches as mpatches
import matplotlib.path as mpath
import matplotlib.pyplot as plt
import numpy as np
from scipy.spatial import ConvexHull
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette — 8 hues, canonical order
IMPRINT_PALETTE = ["#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477", "#99B314"]
# Data — Density (kg/m³) vs Young's Modulus (GPa) for engineering materials
np.random.seed(42)
families = {
"Metals": {
"density": [2700, 4500, 7850, 8900, 7200, 8000, 11340, 1740, 7870, 8940, 2810, 7140, 8500, 4620, 7300],
"modulus": [69, 116, 200, 117, 170, 193, 16, 45, 210, 130, 71, 105, 100, 110, 190],
},
"Polymers": {
"density": [950, 1050, 1200, 1140, 1380, 910, 1420, 1040, 1300, 1170, 980, 1090, 1250, 1060, 1350],
"modulus": [0.9, 2.5, 3.5, 2.8, 3.0, 1.3, 2.9, 2.0, 4.0, 3.2, 0.7, 1.8, 3.8, 2.2, 3.3],
},
"Ceramics": {
"density": [3980, 3200, 2200, 3900, 5680, 2650, 3150, 5900, 2400, 3500, 3100, 4000, 2500, 3700, 2800],
"modulus": [380, 440, 70, 350, 200, 73, 310, 210, 65, 400, 300, 360, 60, 320, 90],
},
"Composites": {
"density": [1600, 1550, 2000, 1800, 1450, 1700, 1900, 1500, 1650, 1850, 1520, 1750, 1400, 1620, 1950],
"modulus": [140, 70, 45, 80, 180, 60, 50, 200, 120, 55, 90, 65, 160, 100, 40],
},
"Elastomers": {
"density": [920, 1100, 1250, 1500, 1050, 1150, 1300, 1000, 1200, 1400, 960, 1080, 1350, 1450, 1180],
"modulus": [0.005, 0.01, 0.05, 0.03, 0.008, 0.02, 0.04, 0.003, 0.015, 0.035, 0.004, 0.012, 0.045, 0.025, 0.007],
},
"Foams": {
"density": [30, 60, 120, 200, 50, 80, 150, 40, 100, 180, 35, 70, 130, 90, 160],
"modulus": [0.001, 0.01, 0.05, 0.2, 0.005, 0.02, 0.1, 0.003, 0.03, 0.15, 0.002, 0.015, 0.06, 0.025, 0.12],
},
"Natural\nMaterials": {
"density": [600, 700, 500, 1200, 800, 450, 650, 1500, 550, 750, 900, 480, 680, 1100, 850],
"modulus": [12, 14, 8, 20, 10, 6, 11, 25, 9, 13, 16, 7, 12.5, 18, 15],
},
}
family_names = list(families.keys())
family_colors = {name: IMPRINT_PALETTE[i] for i, name in enumerate(family_names)}
# Label offsets (log10 coords) to reduce upper-right crowding
label_offsets = {"Metals": (0.30, -0.35), "Ceramics": (-0.25, 0.22), "Composites": (-0.30, -0.15)}
# Plot
fig, ax = plt.subplots(figsize=(8, 4.5), dpi=400, facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)
for family_name, data in families.items():
density = np.array(data["density"], dtype=float)
modulus = np.array(data["modulus"], dtype=float)
color = family_colors[family_name]
ax.scatter(density, modulus, s=80, alpha=0.7, color=color, edgecolors=PAGE_BG, linewidth=0.5, zorder=4)
# Smooth Bezier convex hull envelope using matplotlib Path/PathPatch
log_pts = np.column_stack([np.log10(density), np.log10(modulus)])
rng = np.random.RandomState(hash(family_name) % 2**31)
log_pts_jittered = log_pts + rng.randn(*log_pts.shape) * 0.01
try:
hull = ConvexHull(log_pts_jittered)
hull_verts = np.vstack([log_pts_jittered[hull.vertices], log_pts_jittered[hull.vertices[0]]])
centroid = np.mean(hull_verts[:-1], axis=0)
directions = hull_verts - centroid
norms = np.linalg.norm(directions, axis=1, keepdims=True)
norms = np.where(norms == 0, 1, norms)
hull_verts = hull_verts + directions / norms * 0.08
n_verts = len(hull_verts) - 1
codes = [mpath.Path.MOVETO]
pts = [hull_verts[0]]
for i in range(n_verts):
p0, p1 = hull_verts[i], hull_verts[(i + 1) % n_verts]
pts.extend([p0 + (p1 - p0) * 0.33, p0 + (p1 - p0) * 0.67, p1])
codes.extend([mpath.Path.CURVE4, mpath.Path.CURVE4, mpath.Path.CURVE4])
codes.append(mpath.Path.CLOSEPOLY)
pts.append(pts[0])
pts_arr = np.array(pts)
pts_data = np.column_stack([10 ** pts_arr[:, 0], 10 ** pts_arr[:, 1]])
path = mpath.Path(pts_data, codes)
ax.add_patch(mpatches.PathPatch(path, facecolor=color, edgecolor="none", alpha=0.15, zorder=2))
ax.add_patch(mpatches.PathPatch(path, facecolor="none", edgecolor=color, alpha=0.5, linewidth=1.2, zorder=3))
except Exception:
pass
# Family label at geometric center with optional offset to reduce crowding
cx_log = np.mean(np.log10(density))
cy_log = np.mean(np.log10(modulus))
dx, dy = label_offsets.get(family_name, (0, 0))
ax.text(
10 ** (cx_log + dx),
10 ** (cy_log + dy),
family_name,
fontsize=8,
fontweight="bold",
color=color,
ha="center",
va="center",
zorder=5,
bbox={"boxstyle": "round,pad=0.25", "facecolor": ELEVATED_BG, "edgecolor": "none", "alpha": 0.9},
)
# Guide lines for constant E/rho (lightweight stiffness index)
guide_density = np.logspace(1, 5, 100)
for c_val, label_text in [(0.01, r"$E/\rho = 10$ kPa$\cdot$m$^3$/kg"), (1.0, r"$E/\rho = 1$ GPa$\cdot$m$^3$/Mg")]:
guide_modulus = c_val * guide_density / 1000
mask = (guide_modulus >= 5e-4) & (guide_modulus <= 600)
ax.plot(
guide_density[mask], guide_modulus[mask], color=INK_MUTED, linewidth=0.8, linestyle="--", alpha=0.6, zorder=1
)
valid_idx = np.where(mask)[0]
if len(valid_idx) > 0:
mid = valid_idx[len(valid_idx) // 3]
ax.text(
guide_density[mid],
guide_modulus[mid] * 1.5,
label_text,
fontsize=7,
color=INK_MUTED,
rotation=30,
ha="center",
va="bottom",
)
# Style
title = "scatter-ashby-material · python · matplotlib · anyplot.ai"
title_len = len(title)
title_fs = max(8, round(12 * 67 / title_len)) if title_len > 67 else 12
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlim(10, 30000)
ax.set_ylim(5e-4, 600)
ax.set_xlabel("Density (kg/m$^3$)", fontsize=10, color=INK, labelpad=6)
ax.set_ylabel("Young's Modulus (GPa)", fontsize=10, color=INK, labelpad=6)
ax.set_title(title, fontsize=title_fs, fontweight="medium", color=INK, pad=10)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT, labelcolor=INK_SOFT)
for spine in ax.spines.values():
spine.set_visible(False)
ax.grid(True, which="major", alpha=0.15, linewidth=0.6, color=INK, zorder=0)
ax.grid(True, which="minor", alpha=0.08, linewidth=0.4, color=INK, zorder=0)
plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=400, facecolor=PAGE_BG)
Part of Ashby Material Selection Chart on anyplot.ai.