Added the triangular model to my Ising simulation. The triangular model behave similar to the rectangular model in the ferromagnetic case but in the ant-ferromagnetic case it lacks a base state and continues to have large amounts of noise at arbitrarily low temperatures violating the third law! Video show the difference between the two antiferromagnetic models. The lack of a base state comes from the lack of a 2 - vertex coloring of the triangular graph.
Did you know you can extend the bifurcation diagram for the logistic map
f: z → az(1-z)
beyond a=4 by solving
f^n(z) = z
for various n. The full picture is that for a>4 you get a repelling Cantor set!
Finally finished that Ising model simulation. The reason why I was reading about the ising model is that simple generalizations of it lead to bolzmann and hopfield networks. The Ising model is like a boltzmann network that only remembers the base states, all one spin for J=1 (ferromagnetic) and checkered for J=-1 (antiferromagnetic). This simulation only does Gibbs sampling and I mostly made it as an exercise in c++ but its pretty fun to play with. Since I wrote it in c++ it might be cool to render in opengl and try to get this really performant and dynamic but quadratic complexity and the fact that gibbs samplers cant be parallelized are limitations
It is amazing to me, as someone that has spent his entire life in school, that almost everything I have learned, I learned outside of a classroom on my own prerogative. And now as a graduate student I have to teach and thus be implicit in a lie that wastes the time and potential of young people on worthless pedantry. The lie that a bachelors degree matters at all.
Been writing a simulation of the ising ferromagnetism model in c++ since I realized its been years since I wrote anything in c++ and that's concerning.
Current mood, thankful for modern language features. Going back to c++ has made me feel far more appreciative of rust and its enforcement of safe memory practices. Also, I forgot how ungainly and c++'s feature set is. Its time to stop.
Someone made a flag of #Norway with the NOR gate.
https://cybre.space/@haskal/103434041959654589
Current math phd student. Also likes games and working out.