The Genome in Theodor's Spiral

This visualization converts linear genetic information (DNA/RNA) into a continuous 2D Theodor spiral.

Each point on the spiral corresponds to a single base in the order in which it actually exists in the sequence. The beginning of the sequence is at the center of the spiral. The color of the point represents the base type.

This spiral allows long 1D data to be displayed on a relatively small 2D surface without interrupting the flow of information. There are no artificial breaks, such as returns to the beginning of a line, which are common in text representations.

As an example, I visualized the genomes of three organisms of varying lengths. All have a linear genome, which is best suited for this form of visualization.

HIV-1:

Ebola virus:

SARS-CoV-2:

Source code
The Python source code for this project is available here:

import numpy as np
import matplotlib.pyplot as plt
from collections import Counter
from pathlib import Path

# =========================
# KONFIG
# =========================

SEQ_TXT_PATH = r"ebola_virus_complete_genome.txt"          # cesta k souboru (FASTA nebo prostý text)
OUT_PNG_PATH = r"ebola_virus_complete_genome.png"          # kam uložit PNG výstup

WIDTH_PX  = 4000
HEIGHT_PX = 4000

SHOW_LEGEND = False  # defaultně žádný text
LEGEND_TEXT = "genom na Theodorově spirále"

# RGBK (A,C,G,T/U -> R,G,B,K)
COLORS = {
    "A": (1.0, 0.0, 0.0),  # Red
    "C": (0.0, 1.0, 0.0),  # Green
    "G": (0.0, 0.0, 1.0),  # Blue
    "T": (0.0, 0.0, 0.0),  # Black (Key)
    "U": (0.0, 0.0, 0.0),  # RNA U taky do K
}

# Vzhled
DRAW_SPIRAL_LINE = False
LINE_WIDTH = 0.12
LINE_ALPHA = 0.25

POINT_SIZE = 90.0
POINT_ALPHA = 1

CROP_PADDING_RATIO = 0.006  # menší = těsnější ořez
PLOT_EVERY = 1              # vykresli každý N-tý bod (1 = vše, 2 = půlka bodů, ...)

BACKGROUND = "white"        # nebo "black"
TRANSPARENT_BG = False      # true = průhledné PNG

# =========================
# IMPLEMENTACE
# =========================

def read_sequence(path: str) -> str:
    """Načte sekvenci a nechá jen A/C/G/T/U."""
    txt = Path(path).read_text(encoding="utf-8", errors="ignore").upper()
    seq = "".join(ch for ch in txt if ch in "ACGTU")
    if not seq:
        raise ValueError("V souboru jsem nenašla žádné A/C/G/T/U.")
    return seq

def theodorus_vertices(n: int) -> tuple[np.ndarray, np.ndarray]:
    """Souřadnice vrcholů Theodorovy spirály pro indexy 0..n (0 = origin)."""
    theta = np.zeros(n + 1, dtype=float)
    if n >= 2:
        theta[2:] = np.cumsum(np.arctan(1.0 / np.sqrt(np.arange(1, n))))
    r = np.sqrt(np.arange(0, n + 1, dtype=float))
    x = r * np.cos(theta)
    y = r * np.sin(theta)
    return x, y

def main():
    seq = read_sequence(SEQ_TXT_PATH)
    if PLOT_EVERY > 1:
        seq = seq[::PLOT_EVERY]

    n = len(seq)
    x, y = theodorus_vertices(n)

    pos = np.arange(1, n + 1)  # vrchol i mapuje seq[i-1]
    seq_bytes = np.frombuffer(seq.encode("ascii"), dtype=np.uint8)
    counts = Counter(seq)

    # Figsize = pixely / dpi; dpi si zvolíme jen jako interní převod.
    dpi_internal = 100
    figsize = (WIDTH_PX / dpi_internal, HEIGHT_PX / dpi_internal)

    fig = plt.figure(figsize=figsize, dpi=dpi_internal, facecolor=BACKGROUND)
    ax = fig.add_axes([0, 0, 1, 1])  # žádné okraje, čistý full-bleed
    ax.set_facecolor(BACKGROUND)

    if DRAW_SPIRAL_LINE:
        ax.plot(
            x[1:], y[1:],
            linewidth=LINE_WIDTH,
            color=(0, 0, 0),
            alpha=LINE_ALPHA
        )

    for base in ["A", "C", "G", "T", "U"]:
        mask = (seq_bytes == ord(base))
        if not np.any(mask):
            continue
        idxs = pos[mask]
        ax.scatter(
            x[idxs], y[idxs],
            s=POINT_SIZE,
            c=[COLORS[base]],
            alpha=POINT_ALPHA,
            linewidths=0
        )

    # Tight crop + vycentrování na formát
    xmin, xmax = x[1:].min(), x[1:].max()
    ymin, ymax = y[1:].min(), y[1:].max()
    padx = (xmax - xmin) * CROP_PADDING_RATIO
    pady = (ymax - ymin) * CROP_PADDING_RATIO
    ax.set_xlim(xmin - padx, xmax + padx)
    ax.set_ylim(ymin - pady, ymax + pady)

    ax.set_aspect("equal", adjustable="box")
    ax.axis("off")

    if SHOW_LEGEND:
        title_counts = ", ".join(f"{b}:{counts.get(b, 0)}" for b in ["A", "C", "G", "T", "U"])
        ax.text(
            0.5, 0.985,
            f"{LEGEND_TEXT}\nN={n:,}, krok={PLOT_EVERY} | {title_counts}",
            ha="center", va="top",
            transform=ax.transAxes,
            fontsize=14,
            color="black" if BACKGROUND == "white" else "white"
        )

    fig.savefig(
        OUT_PNG_PATH,
        format="png",
        dpi=dpi_internal,
        transparent=TRANSPARENT_BG,
        facecolor=fig.get_facecolor()
    )
    plt.close(fig)
    print(f"Uloženo: {OUT_PNG_PATH}")

if __name__ == "__main__":
    main()