HARAKU vs Math Surface

HARAKU is an interactive physics simulator that brings wave phenomena to life. Designed for students, educators, and anyone curious about how waves work, HARAKU lets you see and control wave behavior in real time. Developer: Fuji Bit Inc. Part of the educational "Raku" physics series, HARAKU is the wave-physics edition. Whether you are studying for a test, looking for a classroom demo, or simply enjoy how waves behave, HARAKU turns abstract wave equations into vivid, touchable experiences. 10 Simulations: - Superposition: Combine two sine waves and observe constructive and destructive interference. Adjust amplitude, frequency, and phase for each wave independently. - 2D Ripples: Tap to place wave sources on a 2D surface. Watch interference patterns form in real time using finite-difference wave equation solving. Multiple sources create beautiful interference fringes. - Doppler Effect: Drag a moving wave source and observe how wavefronts compress ahead and stretch behind. Two observers show the frequency shift. Push past Mach 1 to see a sonic boom. - Standing Wave: Explore harmonics on a fixed string. See nodes and antinodes appear as you change the harmonic number. Adjust tension and damping to observe how they affect the wave. - Refraction: Visualize Snell's law as a wave crosses between two media. Change the angle of incidence and wave speeds to observe refraction and total internal reflection. - Beat Frequency: Superimpose two waves with slightly different frequencies and watch beats emerge. The red envelope clearly shows the amplitude modulation. - Interference: Watch two-point-source interference fringes form bright (constructive) and dark (destructive) bands. Vary source separation and frequency to see how fringe spacing changes. - Diffraction: A plane wave passes through a slit and spreads out via Huygens' principle. Adjust the slit width relative to the wavelength to see how diffraction strength varies. - Fourier Synthesis: Build square, triangle, and sawtooth waves from a sum of sine harmonics. Increase the harmonic count to watch the synthesis approach the target waveform while seeing each harmonic's contribution. - Reflection: Watch a traveling wave hit a boundary and reflect back. Toggle between fixed-end (phase inverted) and free-end (phase preserved) boundaries to see how the standing wave forms from the incident and reflected waves. Features: - Real-time simulation with smooth 60fps animation - Intuitive parameter sliders for hands-on exploration - Physics info sheets with formulas and explanations - Beautiful dark-themed canvas visualization - Light and Dark mode support - Japanese and English localization (auto-switches by device language) - No sign-up required — open and explore instantly Pricing and Monetization: - Price: Free - In-App Purchases (IAP): None - Ads: A single AdMob banner is shown Part of the "Raku" educational series: - SUUGAKU - Mathematics - BUTURAKU - Mechanics - DENRAKU - Electromagnetism - HARAKU - Wave Physics

3D surfaces, 2D curves, the complex plane, probability — all in one app. Type a formula and watch it come alive. Perfect for study, exploration, or just enjoying the beauty of math. Description: MathSurface turns equations into shapes you can hold, spin, and slice. It's a math playground for iPhone and iPad — designed for students, curious minds, and anyone who learns better by seeing. ■ Features • 3D surface plots: visualize z = f(x, y) with smooth rotation and pinch-to-zoom • 2D function plots: explicit y = f(x) or implicit 0 = F(x, y) curves • Complex plane: loci such as |z − α| = r, arithmetic operations, powers, and n-th roots of unity • Probability distributions: binomial and normal, controlled by live sliders • Surface of revolution: spin any 2D curve around the x- or y-axis (rendered with SceneKit) • Cross sections: slice any 3D surface with a plane and see the resulting curve • Compare mode: overlay two functions in the same plot • Preset gallery: paraboloid, monkey saddle, Mexican hat, lemniscate, and many more • Favorites: save your own custom expressions for instant recall ■ Who it's for • High school and university students studying calculus, analysis, or probability • Teachers looking for live visual aids • Anyone curious about how a formula actually looks • People who just enjoy beautiful math A custom Liquid Glass–style formula keyboard makes entering sin, cos, √, π, and friends quick and natural. The dark neon UI keeps the math front and center.