Polar Heatmap for Cyclic Two-Dimensional Data — Altair

A heatmap wrapped around a circle where the angular axis represents a cyclic variable (e.g., hour of day, month) and the radial axis represents a second categorical or ordinal variable (e.g., day of week, year). Cell color encodes the measured value. This visualization reveals patterns in data with inherent cyclical structure that rectangular heatmaps distort, since the first and last angular bins are visually adjacent rather than separated at opposite ends of a row.

Polar Heatmap for Cyclic Two-Dimensional Data rendered with Altair

Renders

Python source (Altair)

""" anyplot.ai
heatmap-polar: Polar Heatmap for Cyclic Two-Dimensional Data
Library: altair 6.1.0 | Python 3.13.13
Quality: 90/100 | Created: 2026-05-13
"""

import os
import sys


# Prevent the local altair.py from shadowing the installed library
_script_dir = os.path.dirname(os.path.abspath(__file__))
if _script_dir in sys.path:
    sys.path.remove(_script_dir)

import altair as alt
import numpy as np
import pandas as pd


# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"

# Data — monthly energy consumption (kWh) across five years
np.random.seed(42)

months = ["Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"]
years = [2019, 2020, 2021, 2022, 2023]
n_months = len(months)
n_years = len(years)

rows = []
for yi, year in enumerate(years):
    for mi, month in enumerate(months):
        winter = 75 * np.exp(-min(mi**2, (12 - mi) ** 2) / 3.5)
        summer = 45 * np.exp(-((mi - 6.5) ** 2) / 5.0)
        trend = yi * 9
        noise = np.random.normal(0, 10)
        value = round(max(80, 155 + winter + summer + trend + noise), 1)

        rows.append(
            {
                "month": month,
                "year": str(year),
                "value": value,
                "theta": mi * 2 * np.pi / n_months,
                "theta2": (mi + 1) * 2 * np.pi / n_months,
                "r_inner": 100 + yi * 85,
                "r_outer": 100 + (yi + 1) * 85,
            }
        )

df = pd.DataFrame(rows)

# Month label positions (just outside outermost ring at r=525)
month_label_df = pd.DataFrame(
    [
        {"label": month, "theta_mid": (mi + 0.5) * 2 * np.pi / n_months, "r_label": 555}
        for mi, month in enumerate(months)
    ]
)

# Year label positions (near 11 o'clock, in the gap between rings)
year_label_df = pd.DataFrame(
    [
        {"label": str(year), "theta_mid": 2 * np.pi - np.pi / 6, "r_label": 100 + (yi + 0.5) * 85}
        for yi, year in enumerate(years)
    ]
)

# Arc heatmap cells
arc = (
    alt.Chart(df)
    .mark_arc(stroke=PAGE_BG, strokeWidth=0.8)
    .encode(
        theta=alt.Theta("theta:Q", scale=alt.Scale(type="identity")),
        theta2=alt.Theta2("theta2:Q"),
        radius=alt.Radius("r_outer:Q", scale=alt.Scale(type="identity")),
        radius2=alt.Radius2("r_inner:Q"),
        color=alt.Color(
            "value:Q",
            scale=alt.Scale(scheme="viridis"),
            legend=alt.Legend(
                title="kWh / month",
                titleFontSize=18,
                labelFontSize=16,
                fillColor=ELEVATED_BG,
                labelColor=INK_SOFT,
                titleColor=INK,
                strokeColor=INK_SOFT,
                orient="right",
                offset=20,
            ),
        ),
        tooltip=[
            alt.Tooltip("month:N", title="Month"),
            alt.Tooltip("year:N", title="Year"),
            alt.Tooltip("value:Q", title="kWh", format=".0f"),
        ],
    )
)

# Month labels around the perimeter
month_labels = (
    alt.Chart(month_label_df)
    .mark_text(fontSize=18, fontWeight="bold", align="center", baseline="middle", color=INK_SOFT)
    .encode(
        theta=alt.Theta("theta_mid:Q", scale=alt.Scale(type="identity")),
        radius=alt.Radius("r_label:Q", scale=alt.Scale(type="identity")),
        text="label:N",
    )
)

# Year labels near 11 o'clock, one per ring
year_labels = (
    alt.Chart(year_label_df)
    .mark_text(fontSize=16, align="center", baseline="middle", color=INK_SOFT)
    .encode(
        theta=alt.Theta("theta_mid:Q", scale=alt.Scale(type="identity")),
        radius=alt.Radius("r_label:Q", scale=alt.Scale(type="identity")),
        text="label:N",
    )
)

chart = (
    (arc + month_labels + year_labels)
    .properties(
        width=1200,
        height=1200,
        background=PAGE_BG,
        title=alt.Title("heatmap-polar · altair · anyplot.ai", fontSize=28, color=INK, anchor="middle"),
    )
    .configure_view(fill=PAGE_BG, stroke=None)
)

# Save
chart.save(f"plot-{THEME}.png", scale_factor=3.0)
chart.save(f"plot-{THEME}.html")

Part of Polar Heatmap for Cyclic Two-Dimensional Data on anyplot.ai.

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