Magneto Particles (Hodgin Magnetosphere)

Math essence

For each particle i and anchor j, add F = k * sign(q_j) * (anchor_j - pos_i) / ((r_ij^2 + eps)^(3/2)). Add a tangential component t_ij = perpendicular(F_radial) * q_j * tangential_drift. Integrate velocity with global drag and clamp to max_speed, draw a segment from previous to new position with a colour computed from per-particle hue in [0,1).

Parameters

Reference

First 60 lines of reference.py. Full source: library_external/hodgin_iquilezles/MagnetoParticles/reference.py

from __future__ import annotations

from typing import ClassVar

import numpy as np


class MagnetoParticles:
    """Magneto Particles — Robert Hodgin (flight404) *Magnetosphere* lineage, 2006.

    Hodgin's *Magnetosphere* iTunes visualizer is a particle system in which
    every particle carries a small charge and is pulled/pushed by a small
    number of floating magnetic *anchors* whose charges oscillate over time.
    Particles trace a curved, color-tagged trail, producing the iconic
    looping magnetic-field-line look.

    The formula here uses N point sources with per-source attractive or
    repulsive Coulomb-like force  ``F = k * sign(charge) * r̂ / (r^2 + ε)``,
    adds a tangential drift for curvature, and accumulates a low-alpha
    stroke buffer.
    """

    family: ClassVar[str] = "hodgin_iquilezles"
    sketch: ClassVar[str] = "magnetoparticles"

    def __init__(
        self,
        dim: int = 500,
        num: int = 1800,
        num_anchors: int = 6,
        anchor_strength: float = 180.0,
        tangential_drift: float = 0.35,
        drag: float = 0.985,
        max_speed: float = 7.0,
        trail_alpha: int = 32,
        hue_jitter: float = 0.18,
        ink_color: tuple[int, int, int] = (255, 255, 255),
        background: tuple[int, int, int] = (6, 6, 12),
        **_,
    ) -> None:
        self.dim = dim
        self.num = num
        self.num_anchors = num_anchors
        self.anchor_strength = anchor_strength
        self.tangential_drift = tangential_drift
        self.drag = drag
        self.max_speed = max_speed
        self.trail_alpha = trail_alpha
        self.hue_jitter = hue_jitter
        self.ink_color = np.array(ink_color, dtype=np.float32)
        self.bg_color = np.array(background, dtype=np.float32)
        self.reset()

    def reset(self, seed: int | None = None) -> None:
        self.rng = np.random.default_rng(seed)
        self.x = self.rng.uniform(0, self.dim, size=self.num).astype(np.float32)
        self.y = self.rng.uniform(0, self.dim, size=self.num).astype(np.float32)
        a = self.rng.uniform(0, 2 * np.pi, size=self.num)
        s = self.rng.uniform(0.0, 1.5, size=self.num)
        self.vx = (s * np.cos(a)).astype(np.float32)