Lec 11 MIT 18.085 Computational Science and Engineering I
missed out on one that's quite fun uh and uh it leads to uh these fantastic pictures of fractals you may have seen I intended to bring in a book by pipin that has uh sort of the beauty of fractals is his title has pictures of the mandal Bro Set uh just amazing um and just it's interesting mathematics and it's mathematics of recent years so I'm going to put off the wave equation and heat equation to the second lecture today lecture 12 and discuss this one because it's sort of it's so here's the general plan you have some function and you start at some point u0 and you compute F of u0 and that gives the next point then you compute F of U1 and that gives U2 and then you keep going so so u n is so to speak F of f of f of it's where're we're uh we're taking well the mathematical word is composition so so let me just put up U2 so you see U2 U2 is f of f of U uo because that's U1 so we're we're repeating the same operation ...