229 lines
7.7 KiB
HTML
229 lines
7.7 KiB
HTML
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width,initial-scale=1">
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<title>ZKAEDI PRIME — Hamiltonian Self-Similarity Waterfall</title>
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<link href="https://fonts.googleapis.com/css2?family=JetBrains+Mono:wght@400;700&family=Orbitron:wght@700;900&display=swap" rel="stylesheet">
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<style>
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*{box-sizing:border-box;margin:0;padding:0}
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body{background:#000;color:#C8BFAE;font-family:'JetBrains Mono',monospace;font-size:11px;display:flex;flex-direction:column;align-items:center;justify-content:center;height:100vh;overflow:hidden;padding:8px}
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h1{font-family:'Orbitron',monospace;font-size:10px;letter-spacing:4px;color:#CC0030;margin-bottom:3px;text-align:center}
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.sub{font-size:8px;color:#3A3D55;letter-spacing:2px;margin-bottom:8px;text-align:center}
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#c{display:block;border:1px solid #1C1E30}
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.metrics{display:flex;gap:16px;margin-top:8px;font-size:8px;color:#3A3D55;letter-spacing:1px;flex-wrap:wrap;justify-content:center}
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.mv{color:#00BBCC}
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</style>
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</head>
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<body>
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<h1>HAMILTONIAN SELF-SIMILARITY WATERFALL</h1>
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<div class="sub">H_t DECOMPOSED ACROSS SCALES τ=1,2,4,8,16,32 — SELF-SIMILAR STRUCTURE REVEALED</div>
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<canvas id="c"></canvas>
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<div class="metrics">
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FRACTAL DIM: <span class="mv" id="fd">—</span>
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SCALE CORR: <span class="mv" id="sc">—</span>
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HURST (field): <span class="mv" id="hf">—</span>
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DOMINANT SCALE: <span class="mv" id="ds">—</span>
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</div>
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<script>
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const C=document.getElementById('c');
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const ctx=C.getContext('2d');
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const W=Math.min(window.innerWidth-40,680);
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const H=Math.min(window.innerHeight-110,420);
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C.width=W;C.height=H;
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// ZKAEDI PRIME — generate H_t field
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const sigmoid=x=>1/(1+Math.exp(-Math.max(-20,Math.min(20,x))));
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function genHfield(N,eta=0.42,gamma=0.35,beta=0.10,sigma=0.05){
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let seed=7777;
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const rng=()=>{seed=(seed*1664525+1013904223)&0xffffffff;return((seed>>>0)/0xffffffff-.5)*2;};
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const H=new Float64Array(N);
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const H0=0.5;
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H[0]=H0;
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for(let t=1;t<N;t++){
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const sg=sigmoid(gamma*H[t-1]);
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H[t]=H0+eta*H[t-1]*sg+sigma*rng()*(1+beta*Math.abs(H[t-1]));
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}
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return H;
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}
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// Smooth at scale s (box average)
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function smoothAt(H,scale){
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const N=H.length;
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const out=new Float64Array(N);
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for(let i=0;i<N;i++){
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let sum=0,cnt=0;
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for(let k=Math.max(0,i-scale);k<=Math.min(N-1,i+scale);k++){sum+=H[k];cnt++;}
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out[i]=sum/cnt;
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}
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return out;
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}
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// Scale-to-scale correlation
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function corr(a,b){
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const n=Math.min(a.length,b.length);
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let ma=0,mb=0;
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for(let i=0;i<n;i++){ma+=a[i];mb+=b[i];}
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ma/=n;mb/=n;
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let num=0,da=0,db=0;
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for(let i=0;i<n;i++){num+=(a[i]-ma)*(b[i]-mb);da+=(a[i]-ma)**2;db+=(b[i]-mb)**2;}
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return (da>0&&db>0)?num/Math.sqrt(da*db):0;
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}
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const N=600;
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const H=genHfield(N);
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const SCALES=[1,2,4,8,16,32];
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const COLORS=[
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'rgba(0,187,204,0.8)', // τ=1 cyan
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'rgba(0,204,122,0.8)', // τ=2 jade
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'rgba(201,168,76,0.8)', // τ=4 gold
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'rgba(204,85,0,0.8)', // τ=8 amber
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'rgba(148,0,204,0.8)', // τ=16 orchid
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'rgba(204,0,48,0.8)', // τ=32 crimson
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];
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const LABELS=['τ=1','τ=2','τ=4','τ=8','τ=16','τ=32'];
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const scales=SCALES.map(s=>smoothAt(H,s));
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const LAY_H=(H-20)/SCALES.length; // height per scale row
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const PAD_L=52, PAD_R=14, PAD_T=12, PAD_B=20;
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// For each scale, find min/max for scaling
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const stats=scales.map(s=>{
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let mn=Infinity,mx=-Infinity;
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for(const v of s){if(v<mn)mn=v;if(v>mx)mx=v;}
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return{mn,mx};
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});
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// Scale correlations
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const corrs=[];
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for(let i=0;i<scales.length-1;i++) corrs.push(corr(scales[i],scales[i+1]));
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const avgCorr=corrs.reduce((a,b)=>a+b,0)/corrs.length;
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// Hurst of H field
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function simpleHurst(arr){
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const n=arr.length;
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const m=arr.reduce((a,b)=>a+b,0)/n;
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let cum=0,mx=-Infinity,mn=Infinity;
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for(const v of arr){cum+=v-m;if(cum>mx)mx=cum;if(cum<mn)mn=cum;}
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const R=mx-mn;
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const S=Math.sqrt(arr.reduce((a,v)=>a+(v-m)**2,0)/n);
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return S>0?Math.log(R/S)/Math.log(n):0.5;
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}
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const hfHurst=simpleHurst(Array.from(H));
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// Draw background
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ctx.fillStyle='#000';ctx.fillRect(0,0,W,H);
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// Grid lines
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ctx.strokeStyle='rgba(200,191,174,0.04)';ctx.lineWidth=0.5;
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for(let t=0;t<N;t+=60){
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const x=PAD_L+(t/N)*(W-PAD_L-PAD_R);
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ctx.beginPath();ctx.moveTo(x,PAD_T);ctx.lineTo(x,H-PAD_B);ctx.stroke();
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}
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// Draw each scale as filled band + line, waterfall stacked
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for(let si=0;si<scales.length;si++){
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const s=scales[si];
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const {mn,mx}=stats[si];
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const range=mx-mn||1;
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const yBase=PAD_T+si*LAY_H+LAY_H; // bottom of this row
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const yTop=PAD_T+si*LAY_H; // top of this row
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const rowH=LAY_H-1;
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const color=COLORS[si];
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const scale=SCALES[si];
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// Fill band
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ctx.beginPath();
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for(let t=0;t<N;t++){
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const x=PAD_L+(t/N)*(W-PAD_L-PAD_R);
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const yn=yTop+rowH*(1-(s[t]-mn)/range);
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t===0?ctx.moveTo(x,yn):ctx.lineTo(x,yn);
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}
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ctx.lineTo(PAD_L+(N-1)/N*(W-PAD_L-PAD_R),yBase);
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ctx.lineTo(PAD_L,yBase);
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ctx.closePath();
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const grad=ctx.createLinearGradient(0,yTop,0,yBase);
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grad.addColorStop(0,color.replace('0.8','0.18'));
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grad.addColorStop(1,'rgba(0,0,0,0)');
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ctx.fillStyle=grad;ctx.fill();
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// Line
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ctx.beginPath();
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for(let t=0;t<N;t++){
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const x=PAD_L+(t/N)*(W-PAD_L-PAD_R);
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const yn=yTop+rowH*(1-(s[t]-mn)/range);
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t===0?ctx.moveTo(x,yn):ctx.lineTo(x,yn);
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}
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ctx.strokeStyle=color;ctx.lineWidth=si===0?1.2:1.0;ctx.stroke();
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// Row separator
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ctx.strokeStyle='rgba(200,191,174,0.06)';ctx.lineWidth=0.5;
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ctx.beginPath();ctx.moveTo(PAD_L,yBase);ctx.lineTo(W-PAD_R,yBase);ctx.stroke();
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// Label
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ctx.fillStyle=color;ctx.font="bold 8px 'Orbitron'";
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ctx.fillText(LABELS[si],4,yTop+rowH*0.55);
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// Corr with next scale
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if(si<corrs.length){
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ctx.fillStyle='rgba(200,191,174,0.3)';ctx.font="7px 'JetBrains Mono'";
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ctx.fillText('r='+corrs[si].toFixed(2),4,yTop+rowH*0.85);
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}
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// Self-similarity markers: where scale-1 and scale-s are most correlated — highlight peaks
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if(si===0){
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// Mark phase transitions: points where dH/dt spikes
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const dH=[];
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for(let t=1;t<N;t++) dH.push(Math.abs(s[t]-s[t-1]));
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const dMean=dH.reduce((a,b)=>a+b,0)/dH.length;
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const dStd=Math.sqrt(dH.reduce((a,v)=>a+(v-dMean)**2,0)/dH.length);
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for(let t=1;t<N;t++){
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if(dH[t-1]>dMean+2.2*dStd){
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const x=PAD_L+(t/N)*(W-PAD_L-PAD_R);
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ctx.strokeStyle='rgba(204,0,48,0.5)';ctx.lineWidth=1;ctx.setLineDash([1,2]);
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ctx.beginPath();ctx.moveTo(x,PAD_T);ctx.lineTo(x,H-PAD_B);ctx.stroke();ctx.setLineDash([]);
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}
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}
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}
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}
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// Time axis
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ctx.fillStyle='rgba(200,191,174,0.25)';ctx.font="7px 'JetBrains Mono'";
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for(let t=0;t<N;t+=100){
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const x=PAD_L+(t/N)*(W-PAD_L-PAD_R);
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ctx.fillText('t='+t,x-8,H-4);
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}
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ctx.fillText('t →',W-30,H-4);
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// Spectral power analysis (RMS at each scale)
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const powers=scales.map((s,i)=>{
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const mn=stats[i].mn;
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return Math.sqrt(s.reduce((a,v)=>a+(v-mn)**2,0)/N);
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});
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const maxP=Math.max(...powers);
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// Mini power spectrum bar in top-right
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const sbX=W-80,sbY=PAD_T,sbW=60,sbH=40;
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ctx.strokeStyle='rgba(200,191,174,0.1)';ctx.lineWidth=0.5;
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ctx.strokeRect(sbX,sbY,sbW,sbH);
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ctx.fillStyle='rgba(200,191,174,0.15)';ctx.font="6px 'JetBrains Mono'";
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ctx.fillText('POWER',sbX+16,sbY-2);
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for(let si=0;si<SCALES.length;si++){
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const bx=sbX+si*(sbW/SCALES.length)+1;
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const bh=(powers[si]/maxP)*sbH*0.9;
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ctx.fillStyle=COLORS[si].replace('0.8','0.7');
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ctx.fillRect(bx,sbY+sbH-bh,sbW/SCALES.length-2,bh);
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}
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// Fractal dimension estimate: D = 2 - H
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const D=(2-hfHurst).toFixed(3);
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document.getElementById('fd').textContent=D;
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document.getElementById('sc').textContent=avgCorr.toFixed(3);
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document.getElementById('hf').textContent=hfHurst.toFixed(3);
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// Dominant scale: highest power
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const domIdx=powers.indexOf(Math.max(...powers));
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document.getElementById('ds').textContent=LABELS[domIdx];
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</script>
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</body>
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</html>
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