organic
#001
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Sinusoidal Deformation Field
y = sin(x * 0.02 + t) * cos(y * 0.01 + t * 0.5) * 35 + sin(dist(x, y) * 0.05 - t * 2) * 20 Mathematical art made from tiny formulas.
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organic
#002
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Golden Ratio Plant Morphogenesis
θ = n * 137.508°, r = c * √n, x = r * cos(θ + t), y = r * sin(θ + t) organic
#003
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Gielis Morphological Symmetry
r = (|cos(m*φ/4)/a|^n2 + |sin(m*φ/4)/b|^n3)^(-1/n1) organic
#004
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2D Fractal Brownian Flow
angle = fbm(x * 0.003, y * 0.003 + t * 0.15) * 4π, v = [cos(angle), sin(angle)] fluid
#005
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Biot-Savart Point Vortex Dynamics
v_θ(r) = (Γ / 2πr) * (1 - exp(-r² / r_core²)) fluid
#006
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Divergence-Free Solenoidal Flow
vx = (N(x, y+ε) - N(x, y-ε)) / 2ε, vy = -(N(x+ε, y) - N(x-ε, y)) / 2ε fluid
#007
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Discrete Eulerian Advection
ρ_{x,y}^{t+1} = ρ_{x,y}^t * 0.94 + sin(r*0.4 - 3t)*cos(4θ + 2t)*exp(-0.1r)*0.15 fluid
#008
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Stommel-Munk Oceanic Stream Function
u = 2π sin(πx) cos(2πy), v = -π cos(πx) sin(2πy) particles
#009
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Binary Core N-Body Gravity
a_x = G * dx / (dx² + dy² + ε²)^(3/2), a_y = G * dy / (dx² + dy² + ε²)^(3/2) particles
#010
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3D Projected Harmonic Knot Curves
x = sin(3φ + δ), y = sin(4φ), z = cos(5φ + t), px = cx + rotX * depth particles
#011
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Dynamic Euclidean Distance Graph
d = dist(p_i, p_j), if (d < R) drawLine(p_i, p_j, alpha = 1 - d/R) particles
#012
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Craig Reynolds Flocking Algorithm
v += align * 0.05 + cohere * 0.005 + separate * 0.15, p += clamp(v, maxSpeed) geometry
#013
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Conformal Disk Hyperbolic Geometry
r_hyp = R * tanh(l * 0.25 + 0.1 sin(t)), θ = 2πi / p*l + t/l geometry
#014
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Polar Symmetry Modulo Geometry
rotate(2πk / N), drawEllipse(0, r, w * (1 + 0.2 sin(2t + r)), h, rotOffset) geometry
#015
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Superimposed Spatial Frequency Grating
fringe = arc(c1, r) + arc(c2(t), r), beat_frequency = |k1 - k2| geometry
#016
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Recursive Golden Triangle Aperiodic Tiling
p4 = p1 + (p2 - p1) / φ, subdivide(RobinsonTriangle(depth - 1)) waves
#017
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Epicycle Series Waveform Synthesis
r_k = (4 / kπ) * R, x += r_k cos(k t), y += r_k sin(k t), trace(y) waves
#018
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2D Chladni Resonance Nodal Lines
w(x, y) = sin(nπx)*sin(mπy) - sin(mπx)*sin(nπy), p -= ∇|w| * dt waves
#019
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Korteweg-de Vries Non-Linear Wave Dynamics
u(x, t) = 2k² * sech²(k(x - 4k² t)), total_u = u1(x, t) + u2(x, -t) waves
#020
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Bessel Multi-Source Wave Interference
w = Σ (sin(dist_i * freq - 2t) / (sqrt(dist_i)*0.1 + 1)), r_point = 0.5*(w + 1) space
#021
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Schwarzschild Metric Relativistic Deflection
v_orb = 2.5 / √r, y_warp = y - (1.5*rs / d)*22, doppler_hue = 190 + 30*sin(θ) space
#022
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Conic Section Gravitational Ephemerides
E_{k+1} = E_k - (E_k - e*sin(E_k) - M) / (1 - e*cos(E_k)), x = a*cos(E) - ae space
#023
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Lin-Shu Astrophysical Density Wave Theory
armPhase = (1/pitch) * ln(r/10) - 0.4t, r_eff = r * (1 - 0.12 * sin(m*(θ - armPhase))) experimental
#024
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SmoothLife Multi-Kernel Continuous Automata
avg = (1/8) * Σ neighbors, s_{t+1} = (0.25 <= avg <= 0.45) ? s + 0.08 : s - 0.05 experimental
#025
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Complex Dynamic Polynomial Iteration
z = z² + (-0.8 + 0.15 e^(iωt)), iter_escape = min(k | |z_k| > 2) creatures
#026
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Harmonic Umbrella Kinematics & Phosphor Pulse
r_dome = R*(1 + 0.22*sin(3t)), y_tentacle = y0 + s + sin(3t - 6s + k)*18s creatures
#027
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Bilateral Crustacean Gait Kinematics
knee = coxa + [cos(θ)*45 + reach, -20 + lift], pinch = 0.35 + 0.3*sin(3t) creatures
#028
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Segmented Pleon Arching & Pleopod Propulsion
antenna = -s*L - s^1.4*70 + sin(3t - 5s)*18s, pleopod = sin(6t - 0.8s)*0.6 creatures
#029
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Traveling Wave Pectoral Wing Hydrodynamics
wing_z = A(x)*sin(kx - ωt)*exp(-y²/σ²), tail = sin(3t - 4s)*20s creatures
#030
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Equiangular Logarithmic Chamber Geometry
r = a * exp(0.1759 * θ), septum_arch = quadCurve(inPoint, outPoint) botany
#031
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Recursive Lindenmayer Botanical Branching
branch(x, y, len * ratio, angle ± Δθ + wind, depth - 1) botany
#032
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Iterated Function System Botanical Attractor
nextX = 0.85x + 0.04y, nextY = -0.04x + 0.85y + 1.6 (p = 85%) botany
#033
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Trochoidal Deep Water Wave Superposition
x = x0 - (dx/k)*Q*sin(phase), y = y0 - A*cos(phase), phase = k*(dx*x0 + dy*y0) - ωt botany
#034
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Differential Growth Curve & Radial Polyp Bloom
r_ridge = R0 + 12 sin(6θ + 0.5t) + 6 cos(12θ - t), tentacle = quadCurve(mouth, ctrlWave, tip) anatomy
#035
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Electrocardiogram Fourier Waveform & Vascular Rhythm
ecg(t) = P(0.18) + Q(-0.15) + R(1.0) + S(-0.3) + T(0.35), heart_scale = 1 + 0.22*ecg anatomy
#036
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Hodgkin-Huxley Action Potential Transmission
spike = (timer % 2.5) < 0.25, pulse(px, py) = soma_i + (soma_j - soma_i) * (2t % 1) anatomy
#037
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3D Revolving Molecular Helical Geometry
strand1 = [R cos(4πy + 2t), y], strand2 = [R cos(4πy + π + 2t), y], base_rung = line(s1, s2) anatomy
#038
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Pupillary Sphincter & Fractal Collagen Meshwork
pupil_r = R * (0.28 + 0.12*sin(1.5t)), trabecula = quadCurve(pupil, furrow, limbus) fluid
#039
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Rankine Combined Vortex Dynamics & Updraft Physics
v_theta = speed / (0.3 + r*0.7), R_funnel = 20 + z^2.2 * 170, sway = sin(1.5t + 3z)*40z fluid
#040
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Capillary Crown Elevation & Rayleigh-Plateau Jet
crown_h = sin(age * π) * 110, jet_h = sin(jetAge * π) * 160, drop_y += vy*dt + 0.5*g*dt^2 fluid
#041
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Terminal Velocity Vectors & Impact Ripples
y += speed * dt, x += speed * sin(wind) * dt, ripple = ellipse(x, y, r, 0.35r) * exp(-γt) botany
#042
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Brownian Drift Flutter & Parallax Crystals
drift = sin(phase)*1.2 + wind*r*0.8, fy += speed*dt, crystallite = 6_arm_dendrite(r) geometry
#043
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Hexagonal Dendritic Stefan Phase Freezing
main_spine = L*(0.3 + 0.7*growth), prong = spine_pos + [cos(±π/3)*len, sin(±π/3)*len] creatures
#044
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Bathypelagic Esca Photophore & Needle Jaw Array
esca = root + [85 + sin(2.5t)*22, -95 + cos(2t)*16], glow = radialGradient(esca, 12 * (1 + 0.3*sin(4t))) creatures
#045
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Colonial Zooid Helical Chain & Bioluminescent Net
stem = [s*L + sin(1.2t + 4s)*25, sin(4πs + 0.8t)*R], tentilla = [stem.x + sin(2.5t - 6u)*15u, stem.y + u*H] creatures
#046
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Metachronal Ctenes & Rainbow Light Diffraction
ctene_wave = sin(4t - 8s + 0.5r), hue_diffract = (360s + wave*40) % 360 creatures
#047
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Velvety Webbed Cloak & Arm Tip Photophores
web_arch = quadCurve(armTip_a, midPt, armTip_next), photophore = circle(tip, 3.5*(1 + 0.3*sin(4t + a))) creatures
#048
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Ear-Fin Flapping Kinematics & Cirrate Skirt
ear_flap = bezierCurve(root, earCurl*15, earTip + earFlap*26), skirt = quadCurve(arm_prev, midPt - 10, arm_cur) creatures
#049
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Distensible Pelican Jaw & Luminous Whip-Tail
pouch = bezierCurve(top_jaw, 95 + 85*pulse, -10 + 110*pulse, tail_root), tail_organ = radialGradient(tip, 24*pulse) creatures
#050
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Transparent Cranial Shield & Tubular Green Eyes
dome = ellipse(35, -25, 48, 34), tubular_eye = rotate(-π/2 + sin(1.5t)*0.35, green_lens) creatures
#051
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Gymnosome Parapodia Wings & Visceral Core
wing = bezierCurve(root, wingCurl*18, wingTip + wingWave*28), visc_core = radialGradient(5, 2, 22) creatures
#052
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Benthic Fin Stilts & Current Sensing
stilt_fin = quadCurve(pelvic_root, groundContact), prey_sensor = bezierCurve(pectoral_root, wave_tips) creatures
#053
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10-Joint Chebyshev Linkage Deep Sea Stride
knee = coxa + [75*reach, -80*reach + lift], tip = elbow + [35*reach + groundReach, 110*reach] creatures
#054
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Prehensile Tail Spiral & Foliaceous Camouflage
tail = tail_root + [35 - cos(θ)*r, 25 + sin(θ)*r], r = 55 * exp(-0.45*θ), leaf_sway = sin(2.5t + phase)*14 creatures
#055
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Cephalofoil Hydrodynamics & Serpentine Swimming Wave
spine_wave = (x/L)^1.6 * 36 * sin(3.2t - 4*(x/L)), head_t = quadraticCurve(-45, 0, -15, headSpan) physics
#056
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Schrödinger Wavefunction Probability Density Cloud & Spherical Harmonics
P = Math.pow(r*n, l) * Math.exp(-r*2) * Math.abs(Y_lm(theta, phi)) physics
#057
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Non-Linear Dynamical Systems & Butterfly Chaos Theory
dx=s*(y-x)*dt; dy=(x*(r-z)-y)*dt; dz=(x*y-b*z)*dt; physics
#058
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Lagrangian Mechanics & Chaotic Phase Space Orbit
alpha1 = num1(th1,th2,w1,w2)/den1; alpha2 = num2(th1,th2,w1,w2)/den2; physics
#059
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Complex Phasor Harmonic Decomposition & Spectrum Analyzer
z(t) = sum(c_k * exp(i * k * omega * t)) physics
#060
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Orthogonal E & B Vector Fields & Poynting Energy Flow
E(z,t) = E_0 sin(kz - wt) j_hat; B(z,t) = B_0 sin(kz - wt) k_hat; physics
#061
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Einstein Field Equations & Gravitational Lensing Deflection
z(r) = 2 * Math.sqrt(rs * (r - rs)); defAngle = (4 * GM) / (c^2 * b);