Mandelbrot Images generated with “optimized_Fractal_inner_estimate.py”r(N)r(N) calculated with “rN_List.py” Introduction The Mandelbrot set M0M_0 is the set of complex numbers such that for f(z,c)=z2+cf(z,c)=z^2+c the sequence z0(c)=f(0,c),z1(c)=f(f(0,c),c),…,zk(c)=f(zk−1,c),…z_0(c)=f(0,c),z_1(c)=f(f(0,c),c),\dots,z_k(c)=f(z_{k-1},c),\dots doesn’t diverge to infinity.A starting value cc is not in M0M_0 if |zk(c)|>2|z_k(c)|>2 for…
Written by Shahroch Malik Hassany Introduction My task in this project was to understand how a new implementation of the real numbers in Lean works: the ComputableReal Repository. I was supposed to figure out what it does, how it works,…
Written by Vincent Voß, Katrin Weiß This Lean Game was created as a group project during a HEGL seminar by Heide Frank, Johannes Kadel, Adriano Messina, Hannah Rothe, Jonas Schäfer, Alina Stock, Vincent Voß and Katrin Weiß. What is a…
Written by Luca M. Tittel Motivation Braess’s Paradox is a phenomenon rarely witnessed in street-networks or even similar networks like power-networks or some mechanical Systems. It describes the occurrence of the overall flow of a network increasing while the ”capacity”…
Written by Leon-Josip Dzojic, Matilde Sciortino, and Pirmin Kupffer In the year 1980 M. H. Freedman conjectured that every generic smooth knot in three dimensional Euclidean space has a tritangent plane, i.e., a plane tangent to three distinct points. However,…
Written by Aaron Osburg Imagine you are planning your birthday party which will take place in Heidelberg Castle. You have a lot of friends, so you are not quite sure if the inner courtyard of the castle provides enough space…
