A rainflow counting matrix visualizes the results of rainflow cycle counting from a load or stress time history. The matrix displays cycle counts as a 2D heatmap where one axis represents cycle amplitude (half-range), the other represents cycle mean value, and color intensity represents the frequency of each cycle combination. This is a fundamental tool in fatigue analysis and durability engineering, used to characterize variable-amplitude loading for fatigue life prediction.
# anyplot.ai
# heatmap-rainflow: Rainflow Counting Matrix for Fatigue Analysis
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 85/100 | Created: 2026-06-02
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 INK = THEME == "light" ? colorant"#1A1A17" : colorant"#F0EFE8"
const INK_SOFT = THEME == "light" ? colorant"#4A4A44" : colorant"#B8B7B0"
# Imprint sequential colormap for single-polarity continuous data
const ANYPLOT_SEQ = cgrad([colorant"#009E73", colorant"#4467A3"])
# Data: variable-amplitude bridge loading — 200 000 cycles in a 20×20 rainflow matrix
n_amp = 20
n_mean = 20
amp_min = 0.0; amp_max = 200.0 # MPa
mean_min = -50.0; mean_max = 250.0 # MPa
amp_step = (amp_max - amp_min) / n_amp
mean_step = (mean_max - mean_min) / n_mean
amp_centers = [amp_min + (i - 0.5) * amp_step for i in 1:n_amp]
mean_centers = [mean_min + (i - 0.5) * mean_step for i in 1:n_mean]
n_cycles = 200_000
# Exponential amplitude distribution: physically realistic (many small, few large cycles)
amp_raw = clamp.(-35.0 .* log.(rand(n_cycles)), amp_min + 1e-6, amp_max - 1e-6)
# Gaussian mean stress centred at 100 MPa (σ = 45 MPa)
mean_raw = clamp.(randn(n_cycles) .* 45.0 .+ 100.0, mean_min + 1e-6, mean_max - 1e-6)
amp_idx = clamp.(ceil.(Int, (amp_raw .- amp_min) ./ amp_step), 1, n_amp)
mean_idx = clamp.(ceil.(Int, (mean_raw .- mean_min) ./ mean_step), 1, n_mean)
count_matrix = zeros(Int, n_amp, n_mean)
for k in 1:n_cycles
count_matrix[amp_idx[k], mean_idx[k]] += 1
end
# Log10 transform; zero-count bins → NaN (rendered as background color)
count_display = Float64.(count_matrix)
count_display[count_matrix .== 0] .= NaN
count_log = log10.(count_display)
# Contour matrix: replace NaN with 0.0 so iso-lines trace the data boundary cleanly
count_log_contour = ifelse.(isnan.(count_log), 0.0, count_log)
valid_log = filter(!isnan, vec(count_log))
max_log = isempty(valid_log) ? 1.0 : maximum(valid_log)
# Colorbar ticks at decade values within the data range
all_cb_counts = [1, 10, 100, 1_000, 10_000]
all_cb_vals = log10.(Float64.(all_cb_counts))
keep = all_cb_vals .<= max_log + 0.05
cb_vals = all_cb_vals[keep]
cb_labels = string.(all_cb_counts[keep])
# Centroid of the dominant fatigue zone (bins with ≥ 1 000 cycles)
high_mask = count_matrix .>= 1_000
cx_ann = 100.0 # default: Gaussian mean centre
cy_ann = 30.0 # default: low-amplitude region
if any(high_mask)
total_w = Float64(sum(count_matrix[high_mask]))
cx_ann = sum(count_matrix[i, j] * mean_centers[j]
for i in 1:n_amp, j in 1:n_mean if high_mask[i, j]) / total_w
cy_ann = sum(count_matrix[i, j] * amp_centers[i]
for i in 1:n_amp, j in 1:n_mean if high_mask[i, j]) / total_w
end
# Figure: square canvas — 1200×1200 → 2400×2400 at px_per_unit=2
fig = Figure(
size = (1200, 1200),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "Fatigue Spectrum · heatmap-rainflow · julia · makie · anyplot.ai",
titlesize = 19,
titlecolor = INK,
xlabel = "Mean Stress (MPa)",
ylabel = "Cycle Amplitude (MPa)",
xlabelsize = 16,
ylabelsize = 16,
xticklabelsize = 13,
yticklabelsize = 13,
backgroundcolor = PAGE_BG,
topspinevisible = false,
rightspinevisible = false,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
xlabelcolor = INK,
ylabelcolor = INK,
xgridvisible = false,
ygridvisible = false,
)
# heatmap!(ax, x, y, z): x → mean (cols), y → amplitude (rows); z must be (n_mean × n_amp)
hm = heatmap!(
ax,
mean_centers,
amp_centers,
count_log';
colormap = ANYPLOT_SEQ,
nan_color = PAGE_BG,
colorrange = (0.0, max_log),
)
# Contour iso-lines at 100 and 1 000 cycles add visual hierarchy over the heatmap
contour!(
ax,
mean_centers,
amp_centers,
count_log_contour';
levels = [2.0, 3.0],
color = INK_SOFT,
linewidth = 1.5,
)
# Annotate the dominant fatigue region centroid
text!(
ax,
cx_ann, cy_ann + 22.0;
text = "Dominant fatigue\nregion (>1k cycles/bin)",
fontsize = 11,
color = INK,
align = (:center, :bottom),
)
cb = Colorbar(
fig[1, 2],
hm;
label = "Cycle Count",
labelsize = 16,
labelcolor = INK,
ticklabelsize = 13,
ticklabelcolor = INK_SOFT,
tickcolor = INK_SOFT,
ticks = (cb_vals, cb_labels),
)
colgap!(fig.layout, 12)
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/heatmap-rainflow/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": "heatmap-rainflow",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/heatmap-rainflow/julia/makie",
"hub": "https://anyplot.ai/heatmap-rainflow",
"code_json": "https://api.anyplot.ai/specs/heatmap-rainflow/makie/code",
"spec_json": "https://api.anyplot.ai/specs/heatmap-rainflow",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/heatmap-rainflow/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/heatmap-rainflow/julia/makie/plot-dark.png",
"quality_score": 85.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Rainflow Counting Matrix for Fatigue Analysis on anyplot.ai.