Steiner Tree vs Quantum Atlas

This app computes Steiner trees using an evolutionary algorithm. You can place, drag, and delete points of your tree. The optimal number and position of Steiner points is computed. A minimal spanning tree (MST) connects a given set of points in a plane so that the sum of all edges is minimal. Often this sum of all edges can be reduced, if additional points are added. These points are called Steiner points, and the corresponding minimal spanning tree Steiner tree. If more than 3 points are given, it is a hard optimization problem to compute the optimal number and position of Steiner points. This app uses a simple evolutionary algorithm for demonstration purposes. It uses a population of individuals. Each individual represents a MST containing some Steiner points. The population develops towards the optimal Steiner tree in an evolutionary loop: Initially, each individual sets random Steiner points, and constructs the corresponding Steiner tree. The minimal length of the Steiner tree in the population is stored. Each individual has now a fitness value, which is the higher, the closer its Steiner tree length is to the minimal length in the population. Fitter individuals have more descendants by reproduction, and less fit individuals die out. In order to explore better solutions, reproduction does not create descendants that are identical to the parent individual, i.e. do not have their Steiner points at the same position. Rather these positions are shifted randomly by mutation, using a Gaussian distribution. How far they are shifted on average is determined also by their fitness: Good individuals shift their Steiner points less than worse individuals. How fast a good solution is found, depends thus on the population size, and the mutation strength.

Quantum Atlas is a beautiful, pocket-sized reference for the building blocks of reality. From the seventeen particles of the Standard Model to the ideas behind quantum mechanics, field theory, electrodynamics, and the strong force — it turns dense physics into something you can actually explore. And play with. A PERIODIC TABLE FOR PARTICLES Browse all 17 quarks, leptons, and bosons of the Standard Model in a clean, tappable table. Each particle card lays out mass, charge, spin, the forces it feels, its antiparticle, the year and team that discovered it, how it decays, and a plain-English explanation of the role it plays in the universe. No textbook required. LEARN THE CONCEPTS A deck of 12 concept cards covers wavefunctions, superposition, entanglement, spin, uncertainty, tunneling, the photoelectric effect, decoherence, gauge symmetry, vacuum fluctuations, and more — each one designed to be read in a minute and remembered for longer. INTERACTIVE LAB — 22 SIMULATIONS YOU CAN TOUCH Don't just read about physics. Play with it. Every simulation is a real, working experiment that you steer with your finger. The new flagships: • Hydrogen Spectrum — drag an electron between energy levels and watch the photon fall onto its exact wavelength • CHSH Game — a coordination game where classical strategies cap at 75% and entanglement breaks the ceiling at 85.4% The classics: • Double-slit, Mach–Zehnder interferometer, Quantum tunneling • Wave packet spreading, the Uncertainty principle • Spin measurement, Sequential Stern–Gerlach, Bell test • Bloch sphere, Two-state Rabi cycles, Quantum gates playground • Decoherence, Particle in a box, Harmonic oscillator • Photoelectric effect, Blackbody radiation • Atom builder, Orbital shapes • Particle decay tree, Feynman diagram builder GO DEEPER Four theory atlases — 34 entries in all — collect the key results and intuition for each domain: • Quantum Mechanics — wavefunctions, measurement, uncertainty, the foundations • Quantum Field Theory — fields, particles as excitations, virtual processes • Quantum Electrodynamics — photons, vertices, the running of the coupling • Quantum Chromodynamics — quarks, gluons, confinement, asymptotic freedom The Decay Explorer follows 11 unstable particles through their full chains of products, weighted by real measured branching ratios. Run it once and you get one outcome; run it again and you get a different one — exactly like the real universe. The Spectra Explorer renders the real emission lines of 98 elements at their true wavelengths, grouped by periodic-table family — every fingerprint that astronomers actually use to identify atoms across the galaxy. WHO IT'S FOR • Physics students who want to feel concepts, not just read them • Science teachers who need a visual aid that actually demonstrates • Engineers and developers brushing up on quantum • Anyone who has ever wanted to ask "but how does it actually work?" OFFLINE AND PRIVATE No accounts. No ads. No tracking. No analytics. Everything works offline, and nothing about your usage ever leaves your device. SIMPLE, ONE-TIME UNLOCK The Standard Model, the Concepts deck, and the Quantum Mechanics atlas are free, forever. Unlock everything else — the Lab's 22 simulations, the three remaining theory atlases (QFT, QED, QCD), the Decay Explorer, and the Spectra Explorer — with a single one-time purchase. Family Sharing supported. Designed with a premium dark interface, hand-built for iPhone and iPad.