The xkcd color survey

TidyTuesday data for 2025-07-08

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import colors
import colorsys
from sklearn.cluster import KMeans
from sklearn.metrics import pairwise_distances_argmin_min
import textwrap

answers = pd.read_csv('https://raw.githubusercontent.com/rfordatascience/tidytuesday/main/data/2025/2025-07-08/answers.csv')
color_ranks = pd.read_csv('https://raw.githubusercontent.com/rfordatascience/tidytuesday/main/data/2025/2025-07-08/color_ranks.csv')
users = pd.read_csv('https://raw.githubusercontent.com/rfordatascience/tidytuesday/main/data/2025/2025-07-08/users.csv')

answers

	user_id	hex	rank
0	1	#8240EA	1
1	2	#4B31EA	3
2	2	#584601	5
3	2	#DA239C	4
4	2	#B343E5	1
...	...	...	...
1058206	152397	#7238F0	1
1058207	152398	#8E14CD	1
1058208	152398	#0A49E7	3
1058209	152400	#38A30E	2
1058210	152401	#4D004B	1

1058211 rows × 3 columns

answers['rank'].unique()

array([1, 3, 5, 4, 2])

color_ranks

	color	rank	hex
0	purple	1	#7e1e9c
1	green	2	#15b01a
2	blue	3	#0343df
3	pink	4	#ff81c0
4	brown	5	#653700
...	...	...	...
944	fresh green	945	#69d84f
945	electric lime	946	#a8ff04
946	dust	947	#b2996e
947	dark pastel green	948	#56ae57
948	cloudy blue	949	#acc2d9

949 rows × 3 columns

def hex_to_hsl(hex_color):
    rgb = colors.to_rgb(hex_color)  # Returns RGB as floats (0-1)
    h, l, s = colorsys.rgb_to_hls(*rgb)  # Note: HLS order
#    return round(h * 360, 1), round(s * 100, 1), round(l * 100, 1)
    return h, s, l

print(hex_to_hsl("#ff5733"))

(0.02941176470588236, 1.0, 0.6)

# merge answers and color_rank based on rank column
merged_data = pd.merge(answers, color_ranks, on='rank', how='left')
merged_data[['h', 's', 'l']] = merged_data['hex_x'].apply(hex_to_hsl).apply(pd.Series)

merged_data

	user_id	hex_x	rank	color	hex_y	h	s	l
0	1	#8240EA	1	purple	#7e1e9c	0.731373	0.801887	0.584314
1	2	#4B31EA	3	blue	#0343df	0.690090	0.814978	0.554902
2	2	#584601	5	brown	#653700	0.132184	0.977528	0.174510
3	2	#DA239C	4	pink	#ff81c0	0.889800	0.723320	0.496078
4	2	#B343E5	1	purple	#7e1e9c	0.781893	0.757009	0.580392
...	...	...	...	...	...	...	...	...
1058206	152397	#7238F0	1	purple	#7e1e9c	0.719203	0.859813	0.580392
1058207	152398	#8E14CD	1	purple	#7e1e9c	0.776577	0.822222	0.441176
1058208	152398	#0A49E7	3	blue	#0343df	0.619155	0.917012	0.472549
1058209	152400	#38A30E	2	green	#15b01a	0.286353	0.841808	0.347059
1058210	152401	#4D004B	1	purple	#7e1e9c	0.837662	1.000000	0.150980

1058211 rows × 8 columns

merged_data.groupby('color').count()

	user_id	hex_x	rank	hex_y	h	s	l
color
blue	288015	288015	288015	288015	288015	288015	288015
brown	75812	75812	75812	75812	75812	75812	75812
green	314172	314172	314172	314172	314172	314172	314172
pink	131013	131013	131013	131013	131013	131013	131013
purple	249199	249199	249199	249199	249199	249199	249199

f"{merged_data.groupby('color')['hex_x'].nunique().loc['blue']:,}"

'275,337'

cluster_results = {}
for color, group_df in merged_data.groupby('color'):
    kmeans = KMeans(n_clusters=100, random_state=2025)
    kmeans.fit(group_df[['h', 's', 'l']])

    # Store the result: labels and cluster centers
    cluster_results[color] = {
        'labels': kmeans.labels_,
        'centers': kmeans.cluster_centers_,
        'data': group_df.copy()
    }
#    cluster_results[color]['data']['cluster'] = kmeans.labels_

#print(cluster_results["blue"]["data"])

for color in cluster_results:
    group_data = cluster_results[color]['data']
    centers = cluster_results[color]['centers']
    closest_idxs, _ = pairwise_distances_argmin_min(centers, group_data[['h', 's', 'l']].values)
    closest_points = group_data.iloc[closest_idxs]
    cluster_results[color]['closest_points'] = closest_points

print(cluster_results['blue']['closest_points'][['h', 's', 'l']].head(10).values)

[[0.56581741 0.74407583 0.58627451]
 [0.6374269  0.89528796 0.3745098 ]
 [0.50673401 0.52380952 0.62941176]
 [0.59259259 0.54418605 0.42156863]
 [0.66666667 0.88516746 0.59019608]
 [0.66333333 0.20661157 0.4745098 ]
 [0.68726592 0.78070175 0.44705882]
 [0.57042254 0.63963964 0.21764706]
 [0.59777778 0.78947368 0.81372549]
 [0.53159041 0.76884422 0.39019608]]

from scipy.optimize import root_scalar
def hsl_to_rgb(h, s, l):
    # colorsys expects H, L, S in [0,1]
    r, g, b = colorsys.hls_to_rgb(h, l, s)
    return r, g, b
    
# Arc length function of theta
def arc_length(theta, b):
    return (b/2) * (theta * np.sqrt(1 + theta**2) + np.arcsinh(theta))

# Inverse function: find theta given s (arc length)
def theta_for_s(s, b):
    # Use root finding to solve arc_length(theta) - s = 0
    sol = root_scalar(lambda t: arc_length(t, b) - s, bracket=[0, 100], method='bisect')
    return sol.root

d = 4  # distance from center to corner
# Define corner offsets using Cartesian product of [-d, d]
corners = np.array(np.meshgrid([-d, d], [-d, d])).T.reshape(-1, 2)
offsets = np.vstack([[0, 0],corners])

fig, ax = plt.subplots(figsize=(8, 8))

for ind, color_name in enumerate(cluster_results):
    cp = cluster_results[color_name]['closest_points'][['h', 's', 'l']].values
    
    rgb_colors = [hsl_to_rgb(*hsl) for hsl in cp]
    
    b = 0.1  # spiral parameter
    num_points = len(cp)
    desired_sep = 0.3  # desired arc length between points
        
    # Compute theta values for uniform arc length steps
    arc_lengths = np.arange(num_points) * desired_sep
    theta_vals = np.array([theta_for_s(s, b) for s in arc_lengths])
    
    # Compute spiral coords
    r = b * theta_vals
    x = r * np.cos(theta_vals)
    y = r * np.sin(theta_vals)
    
    #plt.scatter(x, y, color=rgb_colors, s=200, marker="|", linewidths=4)
    plt.scatter(x+offsets[ind][0], y+offsets[ind][1], color=rgb_colors, s=100) 
    ax.text(offsets[ind][0], offsets[ind][1]-3.25, f"{color_name}\n{ merged_data.groupby('color')['hex_x'].nunique().loc[color_name]:,}", fontsize=14, ha='center', va='center', color=color_ranks[color_ranks['color'] == color_name]['hex'].values[0], fontfamily="Consolas")

ax.axis("off")
plt.ylim(-7, 7)
plt.xlim(-7, 7)
long_title = "Top 100 of the specified number of color variants selected via K-means clustering for the top five colors in the xkcd color survey."
wrapped_title = "\n".join(textwrap.wrap(long_title, width=60))

plt.title(wrapped_title, fontsize=16, fontfamily="Consolas", loc='left')
plt.tight_layout()
#plt.ylabel("Random value")
plt.savefig("xkcd_colors.png", dpi=300, bbox_inches='tight')
plt.show()