Binary Lambda Calculus and Combinatory Logic
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Transcript of Binary Lambda Calculus and Combinatory Logic
Binary Lambda Calclus and
Combinatory Logic
Presented by Melvin Zhang
by John Tromp in Randomness and Complexity,From Leibniz to Chaitin (2007)
for (int row = 0; row < height; row++) {
for (int col = 0; col < width; col++) {
double c_re = (col - width/2)*4.0/width;
double c_im = (row - height/2)*4.0/width;
double x = 0, y = 0;
double r2;
int iter = 0;
while (x*x+y*y < 4 && iter < max) {
double x_new = x*x-y*y+c_re;
y = 2*x*y+c_im;
x = x_new;
iter++;
}
if (iter < max) pixel(col, row, colors[iter]);
else pixel(col, row, black);
}
}http://jonisalonen.com/2013/lets-draw-the-mandelbrot-set/
https://www.cs.auckland.ac.nz/ chaitin/inv.html
“So I’ve done that using LISP because LISP is simpleenough, LISP is in the intersection between theoreticaland practical programming. Lambda calculus is evensimpler and more elegant than LISP, but it’s unusable.”– An Invitation to Algorithmic Information Theory
Gregory Chaitin