A visualization of the Mandelbrot set, the most iconic fractal in mathematics. Each pixel represents a complex number c on the complex plane, colored by how quickly the iteration z(n+1) = z(n)^2 + c diverges. The boundary between convergent and divergent regions reveals infinitely complex, self-similar structure including the characteristic cardioid and period-2 bulb.
# anyplot.ai
# heatmap-mandelbrot: Mandelbrot Set Fractal Visualization
# Library: makie 0.22.10 | Julia 1.11.9
# Quality: 89/100 | Created: 2026-05-30
using CairoMakie
using Colors
# Theme tokens (Imprint palette — theme-adaptive chrome)
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"
# Imprint sequential colormap: brand green → blue (single-polarity continuous data)
const ANYPLOT_SEQ = cgrad([colorant"#009E73", colorant"#4467A3"])
# Interior of the Mandelbrot set: near-black (canonical convention, never escapes)
const INTERIOR_COLOR = colorant"#0A0A0A"
# Mandelbrot parameters
const X_MIN = -2.5
const X_MAX = 1.0
const Y_MIN = -1.25
const Y_MAX = 1.25
const MAX_ITER = 256
const WIDTH = 1600
const HEIGHT = 900
# Compute smooth escape count for each pixel
xs = range(X_MIN, X_MAX; length = WIDTH)
ys = range(Y_MIN, Y_MAX; length = HEIGHT)
escape = Matrix{Float64}(undef, WIDTH, HEIGHT)
for i in 1:WIDTH, j in 1:HEIGHT
cx = xs[i]
cy = ys[j]
zx = 0.0
zy = 0.0
iter = 0
escaped = false
while iter < MAX_ITER
zx2 = zx * zx
zy2 = zy * zy
if zx2 + zy2 > 4.0
escaped = true
break
end
zy = 2.0 * zx * zy + cy
zx = zx2 - zy2 + cx
iter += 1
end
if escaped
zmod = sqrt(zx * zx + zy * zy)
smooth = iter + 1.0 - log2(log2(zmod))
escape[i, j] = mod(smooth, 8.0) / 8.0
else
escape[i, j] = NaN
end
end
# Figure
fig = Figure(
size = (1600, 900),
fontsize = 14,
backgroundcolor = PAGE_BG,
)
ax = Axis(
fig[1, 1];
title = "heatmap-mandelbrot · julia · makie · anyplot.ai",
titlesize = 20,
titlecolor = INK,
xlabel = "Re(c)",
ylabel = "Im(c)",
xlabelsize = 14,
ylabelsize = 14,
xlabelcolor = INK,
ylabelcolor = INK,
xticklabelsize = 12,
yticklabelsize = 12,
xticklabelcolor = INK_SOFT,
yticklabelcolor = INK_SOFT,
xtickcolor = INK_SOFT,
ytickcolor = INK_SOFT,
leftspinecolor = INK_SOFT,
bottomspinecolor = INK_SOFT,
topspinevisible = false,
rightspinevisible = false,
xgridvisible = false,
ygridvisible = false,
backgroundcolor = PAGE_BG,
aspect = DataAspect(),
)
hm = heatmap!(ax, xs, ys, escape;
colormap = ANYPLOT_SEQ,
nan_color = INTERIOR_COLOR,
colorrange = (0.0, 1.0),
)
Colorbar(fig[1, 2], hm;
label = "Escape speed",
labelsize = 12,
labelcolor = INK,
ticklabelsize = 10,
ticklabelcolor = INK_SOFT,
tickcolor = INK_SOFT,
width = 16,
)
save("plot-$(THEME).png", fig; px_per_unit = 2)
Runnable source as JSON, for any HTTP client: https://api.anyplot.ai/specs/heatmap-mandelbrot/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-mandelbrot",
"language": "julia",
"library": "makie",
"page": "https://anyplot.ai/heatmap-mandelbrot/julia/makie",
"hub": "https://anyplot.ai/heatmap-mandelbrot",
"code_json": "https://api.anyplot.ai/specs/heatmap-mandelbrot/makie/code",
"spec_json": "https://api.anyplot.ai/specs/heatmap-mandelbrot",
"render_light_png": "https://storage.googleapis.com/anyplot-images/plots/heatmap-mandelbrot/julia/makie/plot-light.png",
"render_dark_png": "https://storage.googleapis.com/anyplot-images/plots/heatmap-mandelbrot/julia/makie/plot-dark.png",
"quality_score": 89.0,
"license": "MIT",
"guide": "https://anyplot.ai/llms.txt"
}Part of Mandelbrot Set Fractal Visualization on anyplot.ai.