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What Happens When 4 Light Waves Collide?

BEHIND THE WORK

When four coherent monochromatic light sources emit waves in phase, their wavefronts collide in continuous 3D space to form a breathtaking optical diffraction mandala. Guided by the Helmholtz superposition equation Ψ(x, y) = Σ cos(k · rⱼ), constructive interference creates soaring crystalline wave crests while destructive cancellation carves deep nodal corridors. This video traces the complete 4-source interference wavefield in one unbroken trajectory with exact 0.000mm periodic closure.

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THE MATHEMATICAL RULE

\text{Coherent 4-Source Wave Superposition and Modulated Rosette}

\Psi(x,y)=\sum_{j=1}^4\frac{\cos(k r_j)}{\sqrt{1+0.8 r_j}},\quad r_j=\sqrt{(x-x_j)^2+(y-y_j)^2},\quad (x_j,y_j)\in(\pm d,\pm d)

r(t)=0.54+0.38\cos(28t)+0.045\Psi,\quad \theta(t)=12t+0.08\sin(48t)

\mathbf r(t)=\left(r(t)\cos\theta(t),\, r(t)\sin\theta(t),\, 0.24\Psi\right),\quad 0\leq t\leq 2\pi

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What Happens When 4 Light Waves Collide?

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