{"id":1290,"date":"2009-05-18T11:50:16","date_gmt":"2009-05-18T10:50:16","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=1290"},"modified":"2010-12-21T11:57:51","modified_gmt":"2010-12-21T10:57:51","slug":"plotting-fractals-with-wolfram-alpha","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=1290","title":{"rendered":"Plotting Fractals with Wolfram Alpha"},"content":{"rendered":"

I saw a tweet from someone this morning which mentioned that you could plot the Julia Set<\/a> using Wolfram Alpha.\u00a0 I had to try this for myself as soon as I could and, sure enough, you can plot the Julia set for any complex number Z: -0.765+0.003 I<\/a> for example.<\/p>\n

\"Julia<\/p>\n

Very nice but what else can it do.\u00a0 If I Walpha\u00a0fractals then I get the following output so I’d expect Wolfram Alpha to compute at least the Koch snow flake<\/a>, the Sierpinski gasket<\/a>, the Haferman carpet<\/a> and the curlicue fractal<\/a> and, sure enough, it does (click on the links to see for yourself)<\/p>\n

\"Fractals<\/p>\n

Here is a screenshot for the Koch Fractal.<\/p>\n

\"Koch<\/p>\n

These aren’t the only fractals it knows about though. If you walpha Pentaflake (a fractal close to my heart<\/a>) then you get the following.<\/p>\n

\"A<\/p>\n

Wolfram Alpha can also calculate the H-Fractal<\/a>.<\/p>\n

\"The<\/p>\n

Cantor dust<\/a> is in there too<\/p>\n

\"Cantor<\/p>\n

as is the box fractal<\/a><\/p>\n

\"Box<\/p>\n

\n

It also looks like they are in the middle of implementing the Cesaro fractal<\/a>.\u00a0 If you walpha the term then it tries to generate the fractal for a phase angle of pi\/3 radians and 5 iterations.\u00a0 A few seconds later and the calculation times out.\u00a0 If you lower the number of iterations it returns a red box such as the one below.\u00a0 If my memory serves, Mathematica returns such a box if there is a problem with the graphics output.\u00a0 I hope to see this fixed soon.<\/p>\n

Update:15th July 2009 – The Cesaro Fractal has now been fixed)<\/strong><\/p>\n

\"An<\/a><\/p>\n

It also seems to know about the following fractals but doesn’t seem to calculate anything for them (yet).\u00a0 I say that it seems to know about them because it gives you an input field for ‘Iterations’ which implies that it knows that a number of iterations makes sense in this context.\u00a0 It’ll be cool to see all of these implemented in time.<\/p>\n

(Note: None of these are implemented yet and may never be – I’ll update if that changes)<\/p>\n