A theoretical comparison plot showing Gini impurity and entropy (information gain) as splitting criteria for decision trees across the probability range [0, 1]. Both curves are displayed on the same axes to illustrate their similar behavior and slight differences. This educational visualization helps understand the mathematical foundation of tree-based algorithms and why both criteria lead to similar tree structures in practice.
# anyplot.ai
# line-impurity-comparison: Gini Impurity vs Entropy Comparison
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 87/100 | Created: 2026-05-29
using CairoMakie
using Colors
using Random
Random.seed!(42)
# Theme tokens
const THEME = get(ENV, "ANYPLOT_THEME", "light")
const PAGE_BG = THEME == "light" ? colorant"#FAF8F1" : colorant"#1A1A17"
const ELEVATED_BG = THEME == "light" ? colorant"#FFFDF6" : colorant"#242420"
const INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
const INK_MUTED = THEME == "light" ? colorant"#6B6A63" : colorant"#A8A79F"
const IMPRINT_PALETTE = [
colorant"#009E73",
colorant"#C475FD",
colorant"#4467A3",
colorant"#BD8233",
colorant"#AE3030",
colorant"#2ABCCD",
colorant"#954477",
colorant"#99B314",
]
# Data — probability range, Gini impurity, and normalized binary entropy
p = range(0.0, 1.0; length = 100)
gini_raw = 2 .* p .* (1 .- p)
gini = gini_raw ./ maximum(gini_raw)
entropy_raw = [q <= 0.0 || q >= 1.0 ? 0.0 : -q * log2(q) - (1 - q) * log2(1 - q) for q in p]
entropy = entropy_raw ./ maximum(entropy_raw)
# Plot
title_str = "Gini vs Entropy · line-impurity-comparison · julia · makie · anyplot.ai"
title_n = length(title_str)
title_sz = title_n > 67 ? round(Int, 20 * 67 / title_n) : 20
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = title_str,
titlesize = title_sz,
titlecolor = INK,
xlabel = "Probability p",
ylabel = "Impurity (normalized to [0, 1])",
xlabelsize = 14,
ylabelsize = 14,
xticklabelsize = 12,
yticklabelsize = 12,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xgridvisible = false,
ygridvisible = true,
ygridcolor = RGBAf(INK.r, INK.g, INK.b, 0.15),
xminorgridvisible = false,
yminorgridvisible = false,
)
band!(ax, collect(p), gini, entropy;
color = (IMPRINT_PALETTE[3], 0.12))
lines!(ax, collect(p), gini;
color = IMPRINT_PALETTE[1],
linewidth = 3.0,
label = "Gini: 2p(1−p) [normalized]")
lines!(ax, collect(p), entropy;
color = IMPRINT_PALETTE[2],
linewidth = 3.0,
linestyle = :dash,
label = "Entropy: −p log₂p − (1−p) log₂(1−p)")
# Annotate maximum impurity point at p = 0.5 (spec requirement)
vlines!(ax, [0.5];
color = INK_MUTED,
linewidth = 1.5,
linestyle = :dot)
text!(ax, 0.52, 0.97;
text = "max at p = 0.5",
color = INK_MUTED,
fontsize = 13,
align = (:left, :top))
Legend(fig[1, 2], ax;
framecolor = RGBAf(INK_SOFT.r, INK_SOFT.g, INK_SOFT.b, 0.4f0),
backgroundcolor = ELEVATED_BG,
labelcolor = INK)
# Save
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/line-impurity-comparison/makie/code. Any spec id and library id listed in llms-full.txt fit the same URL shape; every URL below is complete and callable.
{
"spec_id": "line-impurity-comparison",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/line-impurity-comparison/julia/makie",
"hub": "https://anyplot.ai/line-impurity-comparison",
"code_json": "https://api.anyplot.ai/specs/line-impurity-comparison/makie/code",
"spec_json": "https://api.anyplot.ai/specs/line-impurity-comparison",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/line-impurity-comparison/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/line-impurity-comparison/julia/makie/plot-dark.png",
"quality_score": 87.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Gini Impurity vs Entropy Comparison on anyplot.ai.