WoW 6: Gorgeous 4d graphics

May 6, 2009

At some point I should write something about 4d polytopes. They are an incredible work of the human imagination. There are a few places you can find good information on them, just google them.  Or go to the wikipedia page.  If you do the latter you will find some wonderful images.  You might wonder how they were made.  I did, and was very happy for it. Some of them come from an open source application: jenn3d

The still images it produces are beautiful out of the box:

Bi-truncated 8-cell

Bi-truncated 8-cell

Truncated 24-cell

Truncated 24-cell

The great thing is it is open source so you can go in and hack at it to make your own images, it also has a slightly unclear command line format to specify models.

Tetrahedra from truncated 120-cell

Tetrahedra from truncated 120-cell

Maxwell Demon: Website of the week

I am handing out awards, the imaginatively titled “Maxwell’s Demon” website of the week:

wowThere is even a prize, £50.  Though I am lazy so the conditions of this are that the winner:

1) Realises they have won.

2) Contacts me.

3) Puts the logo on their site.

Of course 3 is hard to enforce so you could probably take the money and remove the graphical mess.  I will therefore claim that 3 is to ensure that you are indeed the winner.


WoW 5: Finding numbers

April 30, 2009

Apologies for no website last week, as you can see from my last post but one I was a little busy.

This week we have a technical site, Plouffe’s Inverter, one of those that is not necessarily very interesting until you suddenly need it badly! It is a very neat idea, though.  A database of billions of mathematical constants, from the familiar (\pi, e) to the delightfully abstruse (a search for 1.6184135 gives \ln(Kolakoski)^2*Copeland^2*\Gamma(1/24)^2, maybe this is the constant people are really finding when they think they find the Golden Ratio!

So next time you need to find a number you know where to look!

Maxwell Demon: Website of the week

I am handing out awards, the imaginatively titled “Maxwell’s Demon” website of the week:

wowThere is even a prize, £50.  Though I am lazy so the conditions of this are that the winner:

1) Realises they have won.

2) Contacts me.

3) Puts the logo on their site.

Of course 3 is hard to enforce so you could probably take the money and remove the graphical mess.  I will therefore claim that 3 is to ensure that you are indeed the winner.


WoW 4: Fractals

April 16, 2009

I am often a bit rude about fractal art.  With the right software it becomes easy to create interesting, attractive, complicated images without much thought to what is happening.  It is unfair but I find myself turning away from all of the work, because some of it might perhaps lack rigour.  Just as you might give up on conceptual art after seeing one unmade bed too many.

To redress this balance the winners this week (again its several winners, first to claim gets the prize!) are a couple of sites from artists who clearly engage in the mathematics, creating new objects.  They also have draw dropping rendering skills, that I am very jealous of.

I am going to let the images speak for themselves.  You really should click through for much more goodies.

Ramiro Perez, rfractal

Apollonian Gasket III, Ramiro Perez

Indra 551, Joys Leys

Indra 551, Joys Leys

Double Spiral Shadow Projection, Paul Nylander

Double Spiral Shadow Projection, Paul Nylander

Maxwell Demon: Website of the week

I am handing out awards, the imaginatively titled “Maxwell’s Demon” website of the week:

wowThere is even a prize, £50.  Though I am lazy so the conditions of this are that the winner:

1) Realises they have won.

2) Contacts me.

3) Puts the logo on their site.

Of course 3 is hard to enforce so you could probably take the money and remove the graphical mess.  I will therefore claim that 3 is to ensure that you are indeed the winner.


Unscheduled Post: Hyperbolic Polydron

April 13, 2009

What happens when you put seven equilateral triangles round a point?  

Inspired by sumidiot who was himself inspired by division by zero who were making paper hyperbolic soccer balls, I thought I would put up some pictures of a similar project with polydron.  The construction is simple.  Attach seven triangles round a vertex this gives 7 outside vertices.  Add triangles so these all have exactly seven around them and repeat.  The surface flexes in most interesting ways.

Interestingly it is still an open question whether, assuming zero thickness and perfect hinges, this construction can be continued for ever, embedding a model of the hyperbolic plane in 3 dimensions.  If you take eight triangles round a vertex I believe it is possible as you can regularly fold things up and down.

David Richter has some more thoughts and discussion.

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