A small electronics project from Hacker News this week caught my eye: an LED matrix driven by the phyllotaxis equation — the same math that produces sunflower seeds and pinecone scales.

The Math

Phyllotaxis is deceptively simple:

for n in range(N):
    angle = n * 137.5°
    r = c * sqrt(n)
    x = r * cos(angle)
    y = r * sin(angle)

The 137.5° is the golden angle — the divergence angle that packs circles most densely without overlap. It's why sunflower seeds tile the way they do. The same equation applied to LED positions gives you a visually coherent pattern that feels organic.

The Circuit

• 8x8 LED matrix (WS2812B strip is easier to drive)
• Raspberry Pi Pico as controller ($4)
• 470Ω resistors on each LED if you want visible dimming
• 5V power, 2A supply for 64 LEDs at full brightness

The Code

import time, math
from pimoroni import RGBLED, RGBMatrix

matrix = RGBMatrix(8, 8, pin=0)
matrix.set_brightness(0.3)

GOLDEN = 137.50776405
for n in range(64):
    theta = math.radians(n * GOLDEN)
    r = 0.08 * math.sqrt(n)
    x = int((r * math.cos(theta) + 0.5) * 8)
    y = int((r * math.sin(theta) + 0.5) * 8)
    if 0 <= x < 8 and 0 <= y < 8:
        color = (n % 64, 128, 255 - n % 64)
        matrix.set_pixel(x, y, color[0] // 4, color[1] // 4, color[2] // 4)
        matrix.show()
        time.sleep(0.1)

What I Learned

1. Golden angle is the point. Swap 137.5° for anything else and you get a boring grid or a broken spiral.
2. Sub-pixel dimming matters. The Pi Pico has 16-bit PWM, so brightness steps look smooth. 8-bit PWM is visible.
3. Current draw surprises people. 64 LEDs at 20mA each = 1.28A. If you're on a Pi Pico W USB-C, you need external 5V power or it brownouts.

The Next Step

Animate the phyllotaxis — rotate the golden angle slowly and you get a growing sunflower on a chip. Combined with a real-time clock, you can have it grow during the day and shrink at night. Cheap ambient display, ~$10 total.

Get the AI Agent Automation Guide for the full electronics automation workflow: ggouai.gumroad.com/l/dyrvmg ($17).

Full source: ggouai.top