✨Fourier Integrals and 3D Gaussian Wave Packets✨ Fourier integrals are a way to express complex wave patterns as a sum of simpler sine and cosine waves. Think of it like trying to recreate a complicated sound by combining many pure tones at different frequencies. If you have a function that changes continuously (like a wave or signal), a Fourier integral lets you break it down into these basic building blocks (sine and cosine waves). Instead of just adding up discrete waves (like in Fourier series), you’re adding up a continuous range of them, which is useful for waves that don’t repeat. A Fourier integral is like a recipe that tells you how to mix different waves together to recreate any continuous wave pattern. A Gaussian wave packet is a type of wave that is initially localized (concentrated in a small region) and has a shape that looks like a bell curve (called a Gaussian). In 3D, imagine a little "blob" of waves that spreads out over time. It's localized in space initially but spreads as it moves. This type of wave packet is often used in quantum mechanics to describe particles because it captures both their position and their tendency to spread out. So, a 3D Gaussian wave packet is like a wave “blob” that starts in a specific location and expands over time, and its intensity is distributed in space like a 3D bell curve. Modeled and animated procedurally using #GeometryNodes in #Blender. Music: Me performing Debussy's Clair de Lune 🙃 #math #mathematics #quantummechanics #quantumphysics #physics #wavefunction #fourier #fourieranalysis #integral #calculus #gaussian #complexanalysis #mathvisual #engineering #programming #technicalartist #digitalart #3danimation #mathematicalmodeling #topology #geometry #science #quantumcomputing #education #3dmodeling #procedural #proceduralart - @erik_norman