diff --git a/tools/icons.py b/tools/icons.py
index ebbcaa1..ea00183 100644
--- a/tools/icons.py
+++ b/tools/icons.py
@@ -2,41 +2,62 @@
 
     python3 tools/icons.py            -> icons/icon-512.png, icons/icon-192.png, icons/apple-touch-icon.png
 
-Needs Pillow (pip install pillow). Drawn at 4x and downsampled so the edges are clean.
+Standard library only: three rotated rectangles, 3x3 supersampled, written as RGB PNG.
 """
 import math
-import sys
+import struct
+import zlib
 from pathlib import Path
 
-try:
-    from PIL import Image, ImageDraw
-except ImportError:  # pragma: no cover
-    sys.exit("pip install pillow")
-
 ROOT = Path(__file__).resolve().parent.parent
-GROUND, INK = (11, 11, 14, 255), (237, 240, 240, 255)
+GROUND, INK = (11, 11, 14), (237, 240, 240)
+SS = 3
 
 
-def asterisk(size: int) -> Image.Image:
-    ss = 4
-    W = size * ss
-    im = Image.new("RGBA", (W, W), GROUND)
-    d = ImageDraw.Draw(im)
-    c = W / 2
-    half, width = 150 / 512 * W, 58 / 512 * W     # arm half-length and stroke width, as in icon.svg
-    for k in range(3):
-        a = math.radians(90 + 60 * k)
-        dx, dy = math.cos(a), math.sin(a)
-        nx, ny = -dy * width / 2, dx * width / 2
-        p1 = (c - dx * half, c - dy * half)
-        p2 = (c + dx * half, c + dy * half)
-        d.polygon([(p1[0] + nx, p1[1] + ny), (p2[0] + nx, p2[1] + ny), (p2[0] - nx, p2[1] - ny), (p1[0] - nx, p1[1] - ny)], fill=INK)
-    return im.resize((size, size), Image.LANCZOS)
+def arms(size):
+    """The three arms as (centre, unit direction, half-length, half-width) in pixel units."""
+    c = size / 2
+    half, hw = 150 / 512 * size, 29 / 512 * size
+    return [((c, c), (math.cos(math.radians(90 + 60 * k)), math.sin(math.radians(90 + 60 * k))), half, hw) for k in range(3)]
+
+
+def inside(x, y, shapes):
+    for (cx, cy), (dx, dy), half, hw in shapes:
+        px, py = x - cx, y - cy
+        along, across = px * dx + py * dy, -px * dy + py * dx
+        if abs(along) <= half and abs(across) <= hw:
+            return True
+    return False
+
+
+def asterisk(size):
+    shapes = arms(size)
+    rows = []
+    n = SS * SS
+    for y in range(size):
+        row = bytearray([0])  # PNG filter type 0
+        for x in range(size):
+            hit = 0
+            for sy in range(SS):
+                for sx in range(SS):
+                    if inside(x + (sx + 0.5) / SS, y + (sy + 0.5) / SS, shapes):
+                        hit += 1
+            t = hit / n
+            row.extend(int(round(g + (i - g) * t)) for g, i in zip(GROUND, INK))
+        rows.append(bytes(row))
+    return b"".join(rows)
+
+
+def png(size, raw):
+    def chunk(kind, data):
+        return struct.pack(">I", len(data)) + kind + data + struct.pack(">I", zlib.crc32(kind + data) & 0xFFFFFFFF)
+    ihdr = struct.pack(">IIBBBBB", size, size, 8, 2, 0, 0, 0)
+    return b"\x89PNG\r\n\x1a\n" + chunk(b"IHDR", ihdr) + chunk(b"IDAT", zlib.compress(raw, 9)) + chunk(b"IEND", b"")
 
 
 if __name__ == "__main__":
     out = ROOT / "icons"
     out.mkdir(exist_ok=True)
     for name, size in (("icon-512.png", 512), ("icon-192.png", 192), ("apple-touch-icon.png", 180)):
-        asterisk(size).convert("RGB").save(out / name, optimize=True)
+        (out / name).write_bytes(png(size, asterisk(size)))
         print("built: icons/" + name)