MathVista

MathVista 3D
Particle fir
layer n: rₙ = R (1 − n/N)^α bough: z = zₙ − d u^1.35 heart: x = 16 sin³ u, y = 13 cos u − … snow: z = z₀ − v t

3D particle Christmas tree with heart and snow

3D particle system

The tree is a particle cone: height h from 0 to H, radius r(h) = R (1 − h/H)^α so lower boughs are wide and the crown tapers. Eight spiral arms wrap the cone.

The topper is the classic heart curve x = 16 sin³ u, y = 13 cos u − 5 cos 2u − 2 cos 3u − cos 4u. Snow falls as z − vt; the ground is rings r = r₀ + nΔr with z = A sin(kr − ωt).

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