Example renderings, Space software

Space Software
Mark Dow

Example Space Software renderings

Also see Example Space Software animations

Four Knot 1

Four_knot_1.jpg

A Thue-Morse tiling weave, colored by connectivity.

The motif consists of four chiral spline segments, suggested by a Ted Bell sketch. Why this works (nested circuits in this weave pattern) is a mystery to me. How would a larger Thue-Morse pattern with the same motifs be connected?

Virion structure

P22 bacteriophage, virion structure renderings

P22 bacteriophage virion renderings thumbnail

emd_1222_rendered.jpg

P22 bacteriophage, virion structure animation

P22 bacteriophage virion animation thumbnail

emd_1222_slice_and_roll.swf 2.7 MB, 784 x 588 px.
emd_1222_slice_and_roll_c.avi 14 MB, 784 x 588 px.
A smaller GIF animation of the slices at left.

The virion of P22, a bacteriophage. A virion is the infectious form of a virus as it exists outside the host cell, consisting of a nucleic acid core, and a protein coat.

Rendered from a volumetric Cryo-EM (electon microscope) asymmetric reconstruction.
Data source: EMD_1222, Macromolecular Structure Database.

"The large bulb is the head capsid, containing the DNA injected into the host bacterium, which then commandeers the host cell, turning it into a virus factory. The symmetry of all head capsids of various bacteriophage is icosohedral, made up of large proteins woven together rather like a quilt.

In some cases, the icosohedral symmetry is a little twisted, with hexagonal units wrapped around edges instead of meeting at edges. The corners of the icosohedron are always pentagonal." Steve McQuinn

J.Chang, P.Weigele, J.King, W.Chiu, W.Jiang:
Cryo-EM asymmetric reconstruction of bacteriophage P22 reveals organization of its DNA packaging and infecting machinery. Structure (2006) 14, pp. 1073-1082 [PubMed entry 16730179]

Abstract: "The mechanisms by which most double-stranded DNA viruses package and release their genomic DNA are not fully understood. Single particle cryo-electron microscopy and asymmetric 3D reconstruction reveal the organization of the complete bacteriophage P22 virion, including the protein channel through which DNA is first packaged and later ejected. This channel is formed by a dodecamer of portal proteins and sealed by a tail hub consisting of two stacked barrels capped by a protein needle. Six trimeric tailspikes attached around this tail hub are kinked, suggesting a functional hinge that may be used to trigger DNA release. Inside the capsid, the portal's central channel is plugged by densities interpreted as pilot/injection proteins. A short rod-like density near these proteins may be the terminal segment of the dsDNA genome. The coaxially packed DNA genome is encapsidated by the icosahedral shell. This complete structure unifies various biochemical, genetic, and crystallographic data of its components from the past several decades."
A 3-D tiling based on a logarithmic spiral.
See Logarithmic spirals, waves, and tilings for spiral Matlab code and related logarithmic spirals, images and animations.

3-D spiral tiles


A 3-D tiling, having a self-conjugate surface, based on logarithmic spirals. (stereo pair touching at center, cross-view) Volume data: Violin_tiling.vol.gz	Same surface form, with different coloring, as the tiling to the right. (stereo pair, cross-view) Volume data: Vortex_tiling.vol.gz	Disected element of the tiling to the right. This shape, forms a (monohedral) tiling that fills space with an octahedral symmetry. (stereo pair, cross-view) Rotation movie: Vortex_apple_320x240.wmv Vortex_apple_640x480.wmv Volume data: Vortex_apple.vol.gz	Three tiles (see image at left) interlinked to show how they are rotated and translated to fill space. (stereo pair, cross-view) Rotation movie: Vortex_apple_triple_320x240.wmv Vortex_apple_triple_640x480.wmv Volume data: Vortex_apple_triple.vol.gz (1.5 MB)

Mouse embryo

Mouse_embryo_1a.jpg
Mouse embryo, volume rendered from MRI data. Embryonic age is 23 days after conception.
Also see animated rotation.
Raw volume data available from Caltech Atlas of Mouse Development (data © California Institute of Technology, Pasadena).

Oak cubes

Ambiguous_Triple_Cube.jpg

This form of ambiguity is derived from Oscar Reutersvärd's "Impossible Triangle", which was popularized in the 1950's by Roger Penrose, and is sometimes called a "Penrose Triangle".

Also see Ambiguous Triple Cube animations.

48_Meta-Cube_o4.jpg (small)
48_Meta-Cube.jpg (4 MB, 4900x4900 px.)

16_Rotation_Ambiguous_Cubes_xp4.jpg  (medium)
16_Rotation_Ambiguous_Cubes_o10.jpg  (small)
16_Rotation_Ambiguous_Cubes.jpg  (large)

Rendered from a chunk of DigiMorph CT data of Quercus robur (English or Peduncate Oak): Dr. Peter Gasson, 2002, "Quercus robur" (On-line), Digital Morphology. Accessed October 23, 2006 at http://digimorph.org/specimens/Quercus_robur/. Volume data for the cube: Oak_cube.vol.gz (8 MB).

Knot a trefoil

tritorus_ortho.jpg
This is not an image of a trefoil knot. Three mutally linked and mutually orthogonal tori. See tritorus_ortho_80_20_rotation.avi (3.5 MB) and tritorus_ortho_80_20_slices.avi (4 MB) for other viewpoints.

Human brain, Brodmann areas

Human brain, renderings from T1 weighted MRI, average of 27 scans (Colin, Montreal Neurological Institute, crossed stereo pair) and approximate conjunction with Brodmann areas.

Schematic set of neurons (crossed stereo pair).

neurons_43a_sh.jpg
Schematic set of neurons (crossed stereo pair).

Filtered depth map of colin24 brain.

bcolin24_chips.jpg
Filtered depth map of colin24 brain.

Tetrahedral gasket.

Tetra_5_oversampled8x.jpg
A fifth order Sierpinski tetrahedron. The Matlab function that generated the volume that this image is rendered from is cubic_manifold_general.m, hardcoded for this particular "fractal sponge".

High resolution surface rendering of T1 weighted MRI of head.

dow_MRI_big_head.jpg
High resolution surface rendering of T1 weighted MRI of head.

Rendered brain color coded by Brodmann area.

Brodmann_brain.jpg
Rendered brain color coded by Brodmann area.

Chart showing synaptic (density) development, after Huttenlocher.

Huttenlocher_composite.jpg
Chart showing synaptic (density) development in three brain regions, after Huttenlocher.

axial MRI of human head, 5 different contrasts