Radial HSB RGB Visualization (ChatGPT)

A little chat with ChatGPT 4o returned the following Python code, which I then ran in Google Colab:

import numpy as np
from PIL import Image
import colorsys

# Image size: 4096 x 4096 = 16,777,216 pixels
WIDTH = HEIGHT = 4096
CENTER_X, CENTER_Y = WIDTH // 2, HEIGHT // 2

# Generate all RGB colors
rgb_colors = np.array([[r, g, b] for r in range(256)
                                  for g in range(256)
                                  for b in range(256)], dtype=np.uint8)

# Convert RGB to HSB (HSV), normalized to 0–1 range
def rgb_to_hsv(rgb):
    return np.array([colorsys.rgb_to_hsv(r/255, g/255, b/255) for r, g, b in rgb])

# Convert HSB (HSV) back to RGB 0–255
def hsv_to_rgb(hsv):
    return np.array([colorsys.hsv_to_rgb(h, s, v) for h, s, v in hsv]) * 255

# Convert all RGB to HSV to enable sorting
hsv_colors = rgb_to_hsv(rgb_colors)

# Assign image coordinates to each color using radial HSB mapping
# Hue: angle around center
# Saturation: distance from center
# Brightness: vertical axis (top = bright, bottom = dark)

coords = []
for y in range(HEIGHT):
    for x in range(WIDTH):
        dx = x - CENTER_X
        dy = y - CENTER_Y
        r = np.hypot(dx, dy) / (WIDTH / 2)  # radius as saturation
        theta = (np.arctan2(dy, dx) + np.pi) / (2 * np.pi)  # hue from angle (0–1)
        v = 1.0 - (y / HEIGHT)  # brightness vertically
        coords.append((theta, r, v, x, y))

# Sort all RGB colors by their HSV mapping to the image layout
# Then place each color exactly once
coords.sort()  # sorts by hue, then sat, then bright

# Sort the HSV list the same way to match coordinates
hsv_sorted_idx = np.lexsort((hsv_colors[:, 2], hsv_colors[:, 1], hsv_colors[:, 0]))
rgb_sorted = rgb_colors[hsv_sorted_idx]

# Create image
image = Image.new("RGB", (WIDTH, HEIGHT))
pixels = image.load()

for (h, s, v, x, y), color in zip(coords, rgb_sorted):
    pixels[x, y] = tuple(color)

# Save image (lossless)
image.save("radial_hsb_rgb_visualization.png", "PNG")