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Manta Ray Glide

Elasmobranch batoid kinematics capturing the 2D traveling oscillation waves along flexible pectoral wing margins and fluid wake vortex shedding.

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60 FPS Canvas 2D
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Full Executable Algorithm Code

// 029 - Manta Ray Glide (creatures)
// 1:1 Original algorithm engine source
function createMantaRayGlide() {
  const WING_RIBBONS = 36;
  const TAIL_NODES = 45;
  return {
    setup() {
    },
    render(context, timeState, params) {
      const { ctx, width, height } = context;
      const speed = Number(params.glideSpeed || 1.1);
      const wingSpan = Number(params.wingSpan || 190);
      const t = timeState.time * speed;
      ctx.fillStyle = "#020409";
      ctx.fillRect(0, 0, width, height);
      const cx = width * 0.5;
      const cy = height * 0.48;
      const rotY = Math.sin(t * 0.6) * 0.35;
      const rotX = 0.45 + Math.sin(t * 0.8) * 0.22;
      const rotZ = Math.sin(t * 0.6) * 0.25;
      ctx.save();
      ctx.globalCompositeOperation = "screen";
      const baseHue = (200 + Math.sin(t * 0.7) * 20) % 360;
      for (let r = 0; r < WING_RIBBONS; r++) {
        const normR = (r + 1) / WING_RIBBONS;
        const curSpan = wingSpan * normR;
        const wingFlap = Math.sin(t * 2.8 - normR * 1.6) * (36 * Math.pow(normR, 1.4));
        const wingCurl = Math.cos(t * 2.8 - normR * 1.6) * (20 * normR);
        const steps = 50;
        ctx.beginPath();
        let avgDepth = 0;
        for (let i = 0; i <= steps; i++) {
          const u = i / steps;
          const angle = u * Math.PI * 2;
          const rawX = Math.sin(angle) * curSpan;
          const rawY = -Math.cos(angle) * (65 * normR) + Math.abs(rawX) / curSpan * 25 * normR;
          const rawZ = Math.abs(rawX) / curSpan * wingFlap + rawY / 65 * wingCurl;
          const p = project3D(rawX, rawY, rawZ, rotX, rotY, rotZ, cx, cy, 460, 520);
          avgDepth += p.depth;
          if (i === 0) ctx.moveTo(p.x, p.y);
          else ctx.lineTo(p.x, p.y);
        }
        avgDepth /= steps + 1;
        const ribbonHue = (baseHue + normR * 32) % 360;
        const alpha = (0.05 + normR * 0.32) * avgDepth;
        ctx.strokeStyle = hsla(ribbonHue, 95, 68, alpha);
        ctx.lineWidth = Math.max(0.8, (normR > 0.88 ? 1.8 : 0.9) * avgDepth);
        ctx.stroke();
        if (r % 5 === 0) {
          ctx.fillStyle = hsla(ribbonHue, 90, 50, 0.035 * avgDepth);
          ctx.fill();
        }
      }
      for (let s = -1; s <= 1; s += 2) {
        for (let h = 0; h < 6; h++) {
          const normH = h / 5;
          ctx.beginPath();
          const hornSteps = 12;
          for (let st = 0; st <= hornSteps; st++) {
            const nst = st / hornSteps;
            const hx = s * (12 + normH * 10 + nst * 14);
            const hy = -50 - nst * 30;
            const hz = Math.sin(t * 3.5 + normH * 2 + s + nst * 3) * (8 * nst);
            const p = project3D(hx, hy, hz, rotX, rotY, rotZ, cx, cy, 460, 520);
            if (st === 0) ctx.moveTo(p.x, p.y);
            else ctx.lineTo(p.x, p.y);
          }
          ctx.strokeStyle = hsla((baseHue + 40) % 360, 95, 75, 0.5);
          ctx.lineWidth = 1.2;
          ctx.stroke();
        }
      }
      ctx.beginPath();
      const tailLen = 185;
      for (let n = 0; n <= TAIL_NODES; n++) {
        const normN = n / TAIL_NODES;
        const tx = Math.sin(t * 3.2 - normN * 5) * (26 * normN);
        const ty = 65 + normN * tailLen;
        const tz = Math.cos(t * 2.5 - normN * 6) * (32 * normN);
        const p = project3D(tx, ty, tz, rotX, rotY, rotZ, cx, cy, 460, 520);
        if (n === 0) ctx.moveTo(p.x, p.y);
        else ctx.lineTo(p.x, p.y);
      }
      ctx.strokeStyle = hsla((baseHue + 20) % 360, 95, 80, 0.85);
      ctx.lineWidth = 1.6;
      ctx.stroke();
      ctx.restore();
    }
  };
}

// Default parameters from content metadata
const defaultParams = [
  {
    "key": "glideSpeed",
    "label": "Gliding Rhythm",
    "type": "range",
    "min": 0.4,
    "max": 2.2,
    "step": 0.1,
    "defaultValue": 1.1,
    "description": "Wing flap oscillation cycle"
  },
  {
    "key": "wingSpan",
    "label": "Pectoral Wingspan",
    "type": "range",
    "min": 100,
    "max": 240,
    "step": 10,
    "defaultValue": 180,
    "description": "Hydrodynamic wing tip reach"
  }
];

if (!window.__art_instances) window.__art_instances = {};
if (!window.__art_instances['manta-ray-glide']) {
  const inst = typeof createMantaRayGlide === 'function' ? createMantaRayGlide() : null;
  if (inst && inst.setup) {
    inst.setup({ ctx, width, height, dpr: 1, aspectRatio: width / height }, defaultParams);
  }
  window.__art_instances['manta-ray-glide'] = inst;
}

const instance = window.__art_instances['manta-ray-glide'];
if (instance && instance.render) {
  instance.render(
    { ctx, width, height, dpr: 1, aspectRatio: width / height },
    { time, deltaTime: dt, frameCount: Math.floor(time * 60), fps: 60 },
    defaultParams
  );
}
Edit in Interactive Playground Zero Dependencies • Standalone Canvas 2D
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Mathematical Formulation

medium
Analytical Equation
z(x,y,t)=A(x)sin(kxωt)exp(y2σ2),ptail(s,t)=s+Awsin(ωttskt)z(x, y, t) = A(x) \sin(k x - \omega t) \exp\left(-\frac{y^2}{\sigma^2}\right), \quad \mathbf{p}_{\text{tail}}(s, t) = s + A_w \sin(\omega_t t - s \cdot k_t)
Click to expand
Compact Formula
wing_z = A(x)*sin(kx - ωt)*exp(-y²/σ²), tail = sin(3t - 4s)*20s

Mathematical Tags

#manta-ray #ray #creatures #hydrodynamics #wings #marine
Author: Math Art Core Target: 60 FPS

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