IC 342 by Velimir Popov, Emil Ivanov
Lies at low galactic latitude, only 10.5 degrees from the Galactic Equator, or the Milky Way’s disc plane. Therefore, it is heavily obscured by interstellar matter of the Milky Way.
A Visual History of Supernova, Gamma Ray Burst, and Pulsar Discoveries
This data visualization, created by UC Berkeley grad student Isaac Shivvers, shows a time lapse animation of known supernovae, gamma ray bursts, and pulsars.
The three different visual histories can be viewed here:
Image: A compilation of the different visualizations: supernovae in red, gamma ray bursts in blue, and pulsars in yellow.
My favorite object of the night: NGC 4038. Two colliding galaxies, ripping each other apart with nothing but gravitational tidal forces. Also, the only time the Kelvin filter has looked good
being friends with someone who intimidates you because they’re so amazing
Neil deGrasse Tyson
(via we-are-star-stuff)
M101 LRGB by John.R.Taylor (www.cloudedout.squarespace.com) on Flickr.
girls don’t like boys girls like space travel and natalie dormer
See the evolution of the universe like never before
The cosmic simulation, created by 8,192 computer cores running simultaneously, isn’t perfect but can still offer new insights into our universe.
This is the deepest (and I think the best) view ever obtained of a prominent galaxy Centaurus A.
The image was made heir combined exposure time is in excess of an astonishing 350 hours, or two weeks.
Non-Orientable Surfaces
An orientable surface is a surface on which it’s possible to make a consistent definition of direction. Most surfaces we encounter – like spheres, planes, and tori (doughnut shapes) – are orientable. When visualized in three dimensions, orientable surfaces have two distinct sides.
Non-orientable surfaces, on the other hand, have only one side. From Wikipedia, “The essence of one-sidedness is that [an] ant can crawl from one side of the surface to the ‘other’ without going through the surface or flipping over an edge, but simply by crawling far enough.” At any point on a non-orientable surface it’s impossible to uniquely define, for example, the “clockwise” direction.
The GIFs above show two examples of non-orientable surfaces: a Klein bottle and a Möbius strip.
Mathematica code [Klein Bottle]:
xk[u_, v_] := (-2/15)*Cos[u]*(3*Cos[v] - 30*Sin[u] + 90*Cos[u]^4*Sin[u] - 60*Cos[u]^6*Sin[u] + 5*Cos[u]*Cos[v]*Sin[u]) yk[u_, v_] := (-15^(-1))*Sin[u]*(3*Cos[v] - 3*Cos[u]^2*Cos[v] - 48*Cos[u]^4*Cos[v] + 48*Cos[u]^6*Cos[v] - 60*Sin[u] + 5*Cos[u]*Cos[v]*Sin[u] - 5*Cos[u]^3*Cos[v]*Sin[u] - 80*Cos[u]^5*Cos[v]*Sin[u] + 80*Cos[u]^7*Cos[v]*Sin[u]) zk[u_, v_] := (2/15)*(3 + 5*Cos[u]*Sin[u])*Sin[v] kb[u_, v_] := {xk[u, v], yk[u, v], zk[u, v]} Manipulate[ParametricPlot3D[kb[u, v], {u, 0, umax}, {v, 0, 2*Pi}, PlotRange -> {{-1.8, 2}, {0, 4.5}, {-0.75, 0.75}}, Axes -> False, Boxed -> False, PlotStyle -> {Opacity[0.65]}, Mesh -> {20, 11}, MeshStyle -> Directive[Gray, Opacity[0.65], Thickness[0.003]]], {umax, 0.001, Pi}]Mathematica code [Möbius Strip]:
xm[u_, v_] := (1 + (v/2)*Cos[u/2])*Cos[u] ym[u_, v_] := (1 + (v/2)*Cos[u/2])*Sin[u] zm[u_, v_] := (v/2)*Sin[u/2] ms[u_, v_] := {xm[u, v], ym[u, v], zm[u, v]} Manipulate[ParametricPlot3D[ ms[u, v], {u, 0, umax}, {v, -1, 1}, PlotRange -> {{-1.1, 1.5}, {-1.5, 1.5}, {-0.5, 0.5}}, PlotStyle -> {Opacity[0.65]}, Axes -> False, Boxed -> False, Mesh -> {20, 5}, MeshStyle -> Directive[Gray, Opacity[0.65], Thickness[0.003]]],
{umax, 0.001, 2*Pi}]
Cubes fall through “Flatland”. On the left is a view of the cube in perspective; on the right is a view from directly above which represents what a two-dimensional person viewing the cube from within the plane would be able to perceive.
The top animation shows a square falling through flatland on its face. The slices are always squares. So our two-dimensional person would see “a square existing for a while”.
The second animation shows a square falling through flatland on one of its edges. The slice begins as an edge, then becomes a rectangle; the rectangle grows, becomes a square for a moment, and then gets wider than it is tall. At its widest, it is as wide as the diagonal of one of the square faces of the cube. The rectangle then shrinks back to an edge at the top of the cube.
The third animation is the coolest one! The cube passes through Flatland on one of its corners. In this case, the initial contact is a point, which then becomes a small equilateral triangle. This triangle grows until it touches three of the corners of the cube. At this point, the corners of the triangles begin to be cut off by the other three faces of the cube. For a short moment, the triangle turns into a certain regular polygon... As the cube progresses through the plane, the slice turns again into a cut-off triangle (but inverted with respect to the original one) and finally becomes an equilateral triangle once again as three more vertices pass through the plane. This triangle shrinks down to a point and disappears.
In the third animation, what regular polygon does the triangle turn into halfway through its fall? If you can’t figure out, maybe this artwork by Robert Fathauer will help. (Scroll to the bottom.)
If a 4D cube entered our dimension, what would we see? If you can’t figure this out, check out this awesome page. (Click the GIF links.)