## Christmas greetings – SAGE style

December 12th, 2008 | Categories: general math, sage interactions | Tags:

David Joyner of the SAGE development team has come up with a couple of very nice mathematical Christmas greetings using a combination of SAGE (For the mathematics used to generate the images) and GIMP and Inkscape (for the text).  The first one is based on a Barnsley Fractal and the sage source code is available here.

David’s other creation is a Sierpinski gasket that has been coloured such that it resembles a Christmas tree.  The SAGE source code is given below.

 def sierpinski_seasons_greetings(): """ Code by Marshall Hampton. Colors by David Joyner. General depth by Rob Beezer. Copyright Marshall Hampton 2008, licensed creative commons, attribution share-alike. """ depth = 7 nsq = RR(3^(1/2))/2.0 tlist_old = [[[-1/2.0,0.0],[1/2.0,0.0],[0.0,nsq]]] tlist_new = [x for x in tlist_old] for ind in range(depth): for tri in tlist_old: for p in tri: new_tri = [[(p[0]+x[0])/2.0, (p[1]+x[1])/2.0] for x in tri] tlist_new.append(new_tri) tlist_old = [x for x in tlist_new] T = tlist_old N = 4^depth N1 = N - 3^depth q1 = sum([line(T[i]+[T[i][0]], rgbcolor = (0,1,0)) for i in range(N1)]) q2 = sum([line(T[i]+[T[i][0]], rgbcolor = (1,0,0)) for i in range(N1,N)]) show(q2+q1, figsize = [6,6*nsq], axes = False) 

It just goes to show that advanced mathematical software such as SAGE doesn’t just have to be used for teaching and research – it can be used for making mathematical Christmas cards too! SAGE is completely free and is available from the SAGE math website. Thanks to David for his work on this one.