hypertorus(6x)

📦
version 6.17 · 10 versions
, in fedora 44

💖 hypertorus 💖

okay so we're looking at hypertorus(6x) from the XScreenSaver manual, and bestie. BESTIE. this one is a whole vibe. it's a screensaver module that draws a hypertorus spinning around in 4d and honestly it's giving math-girlie main character energy 🌀✨

✨ NAME ✨

hypertorus — Draws a hypertorus that rotates in 4d

🌸 SYNOPSIS 🌸

hypertorus [--display host:display.screen] [--install] [--visual visual]
           [--window] [--root] [--window-id number] [--delay usecs] [--fps]
           [--wireframe] [--surface] [--transparent] [--solid] [--bands]
           [--spirals-{1,2,4,8,16}] [--torus-knots-{3-2,4-3,5-2,5-3,5-4}]
           [--onesided] [--twosided] [--colorwheel] [--change-colors]
           [--perspective-3d] [--orthographic-3d] [--perspective-4d]
           [--orthographic-4d] [--speed-wx float] [--speed-wy float]
           [--speed-wz float] [--speed-xy float] [--speed-xz float]
           [--speed-yz float]

🦋 DESCRIPTION 🦋

so, the deal: hypertorus shows you the Clifford torus as it rotates in 4d. that's the plot. 🌈

the Clifford torus is a torus that lies on the "surface" of the hypersphere in 4d. yeah. it's that girl. the program projects the 4d torus down to 3d using either a perspective or an orthographic projection — and of those two options, the perspective projection looks much more appealing, no cap. with orthographic projections, the torus degenerates into a doubly covered cylinder at some angles 😭 which is not the slay we're going for. then that projected 3d torus can get projected to the screen either perspectively or orthographically (yes, it's projections all the way down).

there are three display modes for the torus: mesh (wireframe), solid, or transparent. 💅

and on top of that, the appearance of the torus can be a solid object, or a set of see-through bands, see-through spirals, or see-through torus knots. it's giving ✨options✨.

finally (well, for the description at least, don't worry there's more), the colors the torus is drawn with can be set to one-sided, two-sided, or a color wheel. and the colors can be static or changing dynamically.

  • in one-sided color mode, the torus is drawn with the same color on the inside and the outside.
  • in two-sided color mode, the torus is drawn with red on the outside and green on the inside if static colors are used.
  • if changing colors are used, dynamically varying complementary colors are used for the two sides.

and that two-sided mode? it's the one that lets you actually see that the 3d projection of the torus turns inside-out as it rotates in 4d 😵💫 iconic behavior honestly.

the color wheel mode draws the torus with a fully saturated color wheel. if changing colors are used, the colors of the color wheel vary dynamically. and the color wheel mode gives a very nice effect when you combine it with the see-through bands, see-through spirals, or see-through torus knot modes. 🎨

finally finally: the rotation speed for each of the six planes around which the torus rotates can be chosen. 👑

this program is inspired by Thomas Banchoff's book "Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions", Scientific American Library, 1990. shoutout, respectfully. 📚

🎀 OPTIONS 🎀

hypertorus accepts the following options:

  • --window — Draw on a newly-created window. This is the default. (yes she's the default girlie)
  • --root — Draw on the root window.
  • --window-id number — Draw on the specified window.
  • --install — Install a private colormap for the window.
  • --visual visual — Specify which visual to use. Legal values are the name of a visual class, or the id number (decimal or hex) of a specific visual.
  • --delay microseconds — How much of a delay should be introduced between steps of the animation. Default 25000, or 1/40th second.

🌟 the display-mode trio 🌟

The following three options are mutually exclusive. They determine how the torus is displayed. pick one, bestie. 🙈
  • --wireframe — Display the torus as a wireframe mesh.
  • --surface — Display the torus as a solid surface (default).
  • --transparent — Display the torus as a transparent surface.

🌟 the appearance septet 🌟

The following seven options are mutually exclusive. They determine the appearance of the torus. again: ONE. 💅
  • --solid — Display the torus as a solid object.
  • --bands — Display the torus as see-through bands (default).
  • --spirals-1, --spirals-2, --spirals-4, --spirals-8, --spirals-16 — Display the torus as see-through spirals with the indicated number of spirals.
  • --torus-knots-3-2, --torus-knots-4-3, --torus-knots-5-2, --torus-knots-5-3, --torus-knots-5-4 — Display the torus as see-through torus knots. The supported torus knots are (3,2), (4,3), (5,2), (5,3), and (5,4).

🌟 the coloring trio 🌟

The following three options are mutually exclusive. They determine how to color the torus. 🌈
  • --onesided — Display the torus with a single color.
  • --twosided — Display the torus with two colors: one color on the outside and the complementary on the inside. For static colors, the colors are red and green.
  • --colorwheel — Display the torus with a fully saturated color wheel (default). If the torus is displayed as see-through bands, each band will be displayed with a different color. Likewise, if the torus is displayed as see-through spirals, each spiral will receive a different color.

🌟 static colors vs. chaotic colors 🌟

The following options determine whether the colors with which the torus is displayed are static or are changing dynamically.
  • --change-colors — Change the colors with which the torus is displayed dynamically.
  • --no-change-colors — Use static colors to display the torus (default).

🌟 3d → 2d projection 🌟

The following two options are mutually exclusive. They determine how the torus is projected from 3d to 2d (i.e., to the screen).
  • --perspective-3d — Project the torus from 3d to 2d using a perspective projection (default).
  • --orthographic-3d — Project the torus from 3d to 2d using an orthographic projection.

🌟 4d → 3d projection 🌟

The following two options are mutually exclusive. They determine how the torus is projected from 4d to 3d.
  • --perspective-4d — Project the torus from 4d to 3d using a perspective projection (default).
  • --orthographic-4d — Project the torus from 4d to 3d using an orthographic projection.

🌟 the six speed dials 🌟

The following six options determine the rotation speed of the torus around the six possible hyperplanes. The rotation speed is measured in degrees per frame. The speeds should be set to relatively small values, e.g., less than 4 in magnitude. don't be feral about it. 🙏
  • --speed-wx float — Rotation speed around the wx plane (default: 1.1).
  • --speed-wy float — Rotation speed around the wy plane (default: 1.3).
  • --speed-wz float — Rotation speed around the wz plane (default: 1.5).
  • --speed-xy float — Rotation speed around the xy plane (default: 1.7).
  • --speed-xz float — Rotation speed around the xz plane (default: 1.9).
  • --speed-yz float — Rotation speed around the yz plane (default: 2.1).

🌟 extra ✨ 🌟

  • --fps — Display the current frame rate, CPU load, and polygon count.

🖱️ INTERACTION 🖱️

if you run this program in standalone mode you can rotate the hypertorus by dragging the mouse while pressing the left mouse button. this rotates the hypertorus in 3d, i.e., around the wx, wy, and wz planes.

if you press the shift key while dragging the mouse with the left button pressed, the hypertorus is rotated in 4d, i.e., around the xy, xz, and yz planes. 🤯

pro tip from the manpage itself: to examine the hypertorus at your leisure, it is best to set all speeds to 0. otherwise, the hypertorus will rotate while the left mouse button is not pressed. (she does not wait for you, bestie. she's always spinning. 💫)

🌿 ENVIRONMENT 🌿

  • DISPLAY — to get the default host and display number.
  • XENVIRONMENT — to get the name of a resource file that overrides the global resources stored in the RESOURCE_MANAGER property.
  • XSCREENSAVER_WINDOW — The window ID to use with --root.

👀 SEE ALSO 👀

X(1), xscreensaver(1)

Copyright © 2003-2026 by Carsten Steger. Permission to use, copy, modify, distribute, and sell this software and its documentation for any purpose is hereby granted without fee, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation. No representations are made about the suitability of this software for any purpose. It is provided "as is" without express or implied warranty.

👑 AUTHOR 👑

Carsten Steger <carsten@mirsanmir.org>, 04-apr-2026.

and that's the whole page, bestie!! 🫶 this was X Version 11, 6.17-1.fc44 (13-Oct-2026) — mwah, she ate, no crumbs. go spin a 4d torus, you've earned it 💖🎀🦋

📦 where this page comes from