nervous_system_hansmeyer · RadiolarianLattice

Radiolarian Lattice

Nervous System's Radiolaria series translates Ernst Haeckel's 19th-century radiolarian drawings into 3D-printed sculpture. The mathematical heart is a spherical lattice: an icosahedron is recursively subdivided (each face into four triangles), and every new vertex is perturbed along its radial axis by a small random offset, producing a perforated shell whose topology stays regular but whose surface ruffles like a sea creature's silica skeleton. We collapse the 3D body to a 2D orthographic projection with a viewer rotation, then stroke the resulting edges as a wireframe. Color encodes depth — pixels nearer the camera pick up a warm glow accent, far edges fade toward the cool edge color — so the result reads as a translucent geodesic sphere even on a flat substrate.

Original: https://n-e-r-v-o-u-s.com/blog/?p=4601

▶ Try the live demo (JS port) ▶ Run reference.py via Pyodide 10 formulas have instant JS ports. The Pyodide path runs the actual Python in your browser — first load is ~6 MB, then instant.

Family: nervous_system_hansmeyer
Source: nervous system × hansmeyer
Evolution: geometry
Render: wireframe
Complexity: medium
Agents: 642
Year: 2013
Author: Nervous System (Jessica Rosenkrantz & Jesse Louis-Rosenberg)

Math essence

Start with the 12 unit-sphere vertices of a regular icosahedron and its 20 triangular faces. At each subdivision step, every face (a, b, c) is replaced by four triangles using its three edge midpoints (ab, bc, ca) projected back to the unit sphere, growing the vertex count from 12 → 42 → 162 → 642 for k=1,2,3 subdivisions. After subdivision each vertex is displaced along its outward normal: v' = v * (1 + sigma * N(0,1)) + offset_tangent, where the tangent component breaks spherical symmetry so the lattice warps irregularly. Faces are rotated about X and Y axes and orthographically projected to 2D. depth_mix = (z - z_min) / (z_max - z_min) controls per-edge color: foreground edges glow warm, background edges fade to the cool palette color.

Parameters

Name	Type	Default	Range	Description
`dim`	int	`600`	200–1400	Square canvas side length
`subdivisions`	int	`3`	1–5	Number of icosahedron subdivisions (each multiplies vertex count by ~4)
`radial_displacement`	float	`0.18`	0–0.6	Per-vertex radial perturbation magnitude
`displacement_decay`	float	`0.72`	0.2–1	Reserved per-subdivision scaling factor
`projection_axis`	str	`z`	null–null	Orthographic projection axis (x\|y\|z)
`radius`	float	`0.42`	0.15–0.5	Sphere radius as fraction of dim
`edge_color`	tuple	`200,230,255`	null–null	Edge RGB
`glow_color`	tuple	`255,180,110`	null–null	Foreground accent RGB
`bg_color`	tuple	`8,10,18`	null–null	Background RGB
`edge_thickness`	int	`1`	1–3	Edge stroke thickness
`depth_fade`	float	`0.55`	0–1	Depth-mix modulation (0=flat color, 1=high contrast)
`rotation_x`	float	`0.35`	-3.1416–3.1416	View rotation about X axis (radians)
`rotation_y`	float	`0.55`	-3.1416–3.1416	View rotation about Y axis (radians)
`seed`	int	`null`	0–999999	RNG seed

Reference

First 60 lines of reference.py. Full source: library_external/nervous_system_hansmeyer/RadiolarianLattice/reference.py

from __future__ import annotations

from typing import ClassVar

import imageio.v2 as imageio
import numpy as np


def _icosahedron() -> tuple[np.ndarray, np.ndarray]:
    phi = (1.0 + 5.0 ** 0.5) / 2.0
    verts = np.array(
        [
            [-1.0, phi, 0.0],
            [1.0, phi, 0.0],
            [-1.0, -phi, 0.0],
            [1.0, -phi, 0.0],
            [0.0, -1.0, phi],
            [0.0, 1.0, phi],
            [0.0, -1.0, -phi],
            [0.0, 1.0, -phi],
            [phi, 0.0, -1.0],
            [phi, 0.0, 1.0],
            [-phi, 0.0, -1.0],
            [-phi, 0.0, 1.0],
        ],
        dtype=np.float64,
    )
    verts /= np.linalg.norm(verts, axis=1, keepdims=True)
    faces = np.array(
        [
            [0, 11, 5],
            [0, 5, 1],
            [0, 1, 7],
            [0, 7, 10],
            [0, 10, 11],
            [1, 5, 9],
            [5, 11, 4],
            [11, 10, 2],
            [10, 7, 6],
            [7, 1, 8],
            [3, 9, 4],
            [3, 4, 2],
            [3, 2, 6],
            [3, 6, 8],
            [3, 8, 9],
            [4, 9, 5],
            [2, 4, 11],
            [6, 2, 10],
            [8, 6, 7],
            [9, 8, 1],
        ],
        dtype=np.int64,
    )
    return verts, faces


class RadiolarianLattice:
    family: ClassVar[str] = "nervous_system_hansmeyer"
    sketch: ClassVar[str] = "RadiolarianLattice"

Try running it locally

The reference implementation is self-contained Python with numpy. Install the package and run:

python library_external/nervous_system_hansmeyer/RadiolarianLattice/reference.py

Need help? See Learn for the standard environment setup, or Playground for an in-browser sketchbook.

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