Romeo & Juliet phase portrait

readme.md

In 1988, Steven Strogatz proposed using two people’s changing feelings for each other over time as an example for teaching ordinary differential equations. Read his eloquent one-page note.

Each person has two personality parameters determining whether they respond positively or negatively to their own feelings for someone else, and whether they respond positively or negatively to another person’s feelings for them. They also have some initial conditions here (first impressions of each other, you could say), though in a larger model you might want everyone to start at apathy and ignorance.

So if t is time; R is Romeo’s feelings for Juliet; J is Juliet’s feelings for Romeo; and a, b, c, and d are personality parameters; you have:

dR/dt = aR + bJ
dJ/dt = cR + dJ

I think I first came across this in Prof. Pietraho and Prof. Zeeman’s classes at Bowdoin. I think it was on a final exam. J. C. Sprott has a good exposition of Strogatz’s model here.

Of course this is all very silly. But I like exercising a more dynamic vocabulary for relationship state than the static “being together” or “not being together”. I like thinking about orbits. There is something romantic about constant freefall under centripedal acceleration toward your mutual baryocenter. And I like puns about three-body systems.

But if there is one way in which math classes shaped my mind in a way unfit for relationships with people, it is the focus on the limiting behavior of systems. There is a lot of fatalism in math: either something will converge as t approaches infinity, or it will diverge. But sometimes things converge very slowly! I guess this is an embarrassing error, but I think I internalized the asymptotic outlook to such an extent that hearing someone in my life on Earth say “timing is everything” is somehow jarring.

Math is necessary, universal, and eternal. Love is contingent, personal, and fleeting. In math, anything that isn’t always true is dishonest. In love, anything that would be true for anyone else is dishonest. In math, your proof should hold true for anyone, anywhere, at any time. In love, you are at your most honest when your words would be lies, or devoid of meaning, if they were said to anyone else, or at any other time.

Anyway, I know very little of either. There are probably bugs in here. Good chance something’s entirely upside-down.

—14 February 02016

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a[this.color]||this.color}};t.exports=h},{}],5:[function(e,t,i){function h(e,t,i){var a="KaTeX parse error: "+e;if(t!==undefined&&i!==undefined){a+=" at position "+i+": ";var r=t._input;r=r.slice(0,i)+"\u0332"+r.slice(i);var l=Math.max(0,i-15);var s=i+15;a+=r.slice(l,s)}var p=new Error(a);p.name="ParseError";p.__proto__=h.prototype;p.position=i;return p}h.prototype.__proto__=Error.prototype;t.exports=h},{}],6:[function(e,t,i){var h=e("./functions");var a=e("./environments");var r=e("./Lexer");var l=e("./symbols");var s=e("./utils");var p=e("./parseData");var c=e("./ParseError");function n(e,t){this.lexer=new r(e);this.settings=t}var o=p.ParseNode;var g=p.ParseResult;function d(e,t){this.result=e;this.isFunction=t}n.prototype.expect=function(e,t){if(e.text!==t){throw new c("Expected '"+t+"', got '"+e.text+"'",this.lexer,e.position)}};n.prototype.parse=function(e){var t=this.parseInput(0,"math");return t.result};n.prototype.parseInput=function(e,t){var i=this.parseExpression(e,t,false);this.expect(i.peek,"EOF");return i};var w=["}","\\end","\\right","&","\\\\","\\cr"];n.prototype.parseExpression=function(e,t,i,h){var a=[];var r=null;while(true){r=this.lexer.lex(e,t);if(w.indexOf(r.text)!==-1){break}if(h&&r.text===h){break}var l=this.parseAtom(e,t);if(!l){if(!this.settings.throwOnError&&r.text[0]==="\\"){var s=this.handleUnsupportedCmd(r.text,t);a.push(s);e=r.position;continue}break}if(i&&l.result.type==="infix"){break}a.push(l.result);e=l.position}var p=new g(this.handleInfixNodes(a,t),e);p.peek=r;return p};n.prototype.handleInfixNodes=function(e,t){var i=-1;var a;var r;for(var l=0;l<e.length;l++){var s=e[l];if(s.type==="infix"){if(i!==-1){throw new c("only one infix operator per group",this.lexer,-1)}i=l;r=s.value.replaceWith;a=h.funcs[r]}}if(i!==-1){var p,n;var g=e.slice(0,i);var d=e.slice(i+1);if(g.length===1&&g[0].type==="ordgroup"){p=g[0]}else{p=new o("ordgroup",g,t)}if(d.length===1&&d[0].type==="ordgroup"){n=d[0]}else{n=new o("ordgroup",d,t)}var w=a.handler(r,p,n);return[new o(w.type,w,t)]}else{return e}};var u=1;n.prototype.handleSupSubscript=function(e,t,i,a){var r=this.parseGroup(e,t);if(!r){var l=this.lexer.lex(e,t);if(!this.settings.throwOnError&&l.text[0]==="\\"){return new g(this.handleUnsupportedCmd(l.text,t),l.position)}else{throw new c("Expected group after '"+i+"'",this.lexer,e)}}else if(r.isFunction){var s=h.funcs[r.result.result].greediness;if(s>u){return this.parseFunction(e,t)}else{throw new c("Got function '"+r.result.result+"' with no arguments "+"as "+a,this.lexer,e)}}else{return r.result}};n.prototype.handleUnsupportedCmd=function(e,t){var i=[];for(var h=0;h<e.length;h++){i.push(new o("textord",e[h],"text"))}var a=new o("text",{body:i,type:"text"},t);var r=new o("color",{color:this.settings.errorColor,value:[a],type:"color"},t);return r};n.prototype.parseAtom=function(e,t){var i=this.parseImplicitGroup(e,t);if(t==="text"){return i}var h;if(!i){h=e;i=undefined}else{h=i.position}var a;var r;var l;while(true){var s=this.lexer.lex(h,t);if(s.text==="\\limits"||s.text==="\\nolimits"){if(!i||i.result.type!=="op"){throw new c("Limit controls must follow a math operator",this.lexer,h)}else{var p=s.text==="\\limits";i.result.value.limits=p;i.result.value.alwaysHandleSupSub=true;h=s.position}}else if(s.text==="^"){if(a){throw new c("Double superscript",this.lexer,h)}l=this.handleSupSubscript(s.position,t,s.text,"superscript");h=l.position;a=l.result}else if(s.text==="_"){if(r){throw new c("Double subscript",this.lexer,h)}l=this.handleSupSubscript(s.position,t,s.text,"subscript");h=l.position;r=l.result}else if(s.text==="'"){var n=new o("textord","\\prime",t);var d=[n];h=s.position;while((s=this.lexer.lex(h,t)).text==="'"){d.push(n);h=s.position}a=new o("ordgroup",d,t)}else{break}}if(a||r){return new g(new o("supsub",{base:i&&i.result,sup:a,sub:r},t),h)}else{return i}};var k=["\\tiny","\\scriptsize","\\footnotesize","\\small","\\normalsize","\\large","\\Large","\\LARGE","\\huge","\\Huge"];var m=["\\displaystyle","\\textstyle","\\scriptstyle","\\scriptscriptstyle"];n.prototype.parseImplicitGroup=function(e,t){var i=this.parseSymbol(e,t);if(!i||!i.result){return this.parseFunction(e,t)}var h=i.result.result;var r;if(h==="\\left"){var l=this.parseFunction(e,t);r=this.parseExpression(l.position,t,false);this.expect(r.peek,"\\right");var p=this.parseFunction(r.position,t);return new g(new o("leftright",{body:r.result,left:l.result.value.value,right:p.result.value.value},t),p.position)}else if(h==="\\begin"){var n=this.parseFunction(e,t);var d=n.result.value.name;if(!a.hasOwnProperty(d)){throw new c("No such environment: "+d,this.lexer,n.result.value.namepos)}var w=a[d];var u=[null,t,d];var f=this.parseArguments(n.position,t,"\\begin{"+d+"}",w,u);u[0]=f;var v=w.handler.apply(this,u);var y=this.lexer.lex(v.position,t);this.expect(y,"\\end");var x=this.parseFunction(v.position,t);if(x.result.value.name!==d){throw new c("Mismatch: \\begin{"+d+"} matched "+"by \\end{"+x.result.value.name+"}",this.lexer,x.namepos)}v.position=x.position;return v}else if(s.contains(k,h)){r=this.parseExpression(i.result.position,t,false);return new g(new o("sizing",{size:"size"+(s.indexOf(k,h)+1),value:r.result},t),r.position)}else if(s.contains(m,h)){r=this.parseExpression(i.result.position,t,true);return new g(new o("styling",{style:h.slice(1,h.length-5),value:r.result},t),r.position)}else{return this.parseFunction(e,t)}};n.prototype.parseFunction=function(e,t){var i=this.parseGroup(e,t);if(i){if(i.isFunction){var a=i.result.result;var r=h.funcs[a];if(t==="text"&&!r.allowedInText){throw new c("Can't use function '"+a+"' in text mode",this.lexer,i.position)}var l=[a];var s=this.parseArguments(i.result.position,t,a,r,l);var p=h.funcs[a].handler.apply(this,l);return new g(new o(p.type,p,t),s)}else{return i.result}}else{return null}};n.prototype.parseArguments=function(e,t,i,a,r){var l=a.numArgs+a.numOptionalArgs;if(l===0){return e}var s=e;var p=a.greediness;var n=[s];for(var o=0;o<l;o++){var w=a.argTypes&&a.argTypes[o];var u;if(o<a.numOptionalArgs){if(w){u=this.parseSpecialGroup(s,w,t,true)}else{u=this.parseOptionalGroup(s,t)}if(!u){r.push(null);n.push(s);continue}}else{if(w){u=this.parseSpecialGroup(s,w,t)}else{u=this.parseGroup(s,t)}if(!u){var k=this.lexer.lex(s,t);if(!this.settings.throwOnError&&k.text[0]==="\\"){u=new d(new g(this.handleUnsupportedCmd(k.text,t),k.position),false)}else{throw new c("Expected group after '"+i+"'",this.lexer,e)}}}var m;if(u.isFunction){var f=h.funcs[u.result.result].greediness;if(f>p){m=this.parseFunction(s,t)}else{throw new c("Got function '"+u.result.result+"' as "+"argument to '"+i+"'",this.lexer,u.result.position-1)}}else{m=u.result}r.push(m.result);n.push(m.position);s=m.position}r.push(n);return s};n.prototype.parseSpecialGroup=function(e,t,i,h){if(t==="original"){t=i}if(t==="color"||t==="size"){var a=this.lexer.lex(e,i);if(h&&a.text!=="["){return null}this.expect(a,h?"[":"{");var r=this.lexer.lex(a.position,t);var l;if(t==="color"){l=r.text}else{l=r.data}var s=this.lexer.lex(r.position,i);this.expect(s,h?"]":"}");return new d(new g(new o(t,l,i),s.position),false)}else if(t==="text"){var p=this.lexer.lex(e,"whitespace");e=p.position}if(h){return this.parseOptionalGroup(e,t)}else{return this.parseGroup(e,t)}};n.prototype.parseGroup=function(e,t){var i=this.lexer.lex(e,t);if(i.text==="{"){var h=this.parseExpression(i.position,t,false);var a=this.lexer.lex(h.position,t);this.expect(a,"}");return new d(new g(new o("ordgroup",h.result,t),a.position),false)}else{return this.parseSymbol(e,t)}};n.prototype.parseOptionalGroup=function(e,t){var i=this.lexer.lex(e,t);if(i.text==="["){var h=this.parseExpression(i.position,t,false,"]");var a=this.lexer.lex(h.position,t);this.expect(a,"]");return new d(new g(new o("ordgroup",h.result,t),a.position),false)}else{return null}};n.prototype.parseSymbol=function(e,t){var i=this.lexer.lex(e,t);if(h.funcs[i.text]){return new d(new g(i.text,i.position),true)}else if(l[t][i.text]){return new d(new g(new o(l[t][i.text].group,i.text,t),i.position),false)}else{return null}};n.prototype.ParseNode=o;t.exports=n},{"./Lexer":3,"./ParseError":5,"./environments":15,"./functions":18,"./parseData":20,"./symbols":22,"./utils":23}],7:[function(e,t,i){function h(e,t){return e===undefined?t:e}function a(e){e=e||{};this.displayMode=h(e.displayMode,false);this.throwOnError=h(e.throwOnError,true);this.errorColor=h(e.errorColor,"#cc0000")}t.exports=a},{}],8:[function(e,t,i){function h(e,t,i,h){this.id=e;this.size=t;this.cramped=h;this.sizeMultiplier=i}h.prototype.sup=function(){return w[u[this.id]]};h.prototype.sub=function(){return w[k[this.id]]};h.prototype.fracNum=function(){return w[m[this.id]]};h.prototype.fracDen=function(){return w[f[this.id]]};h.prototype.cramp=function(){return w[v[this.id]]};h.prototype.cls=function(){return g[this.size]+(this.cramped?" cramped":" uncramped")};h.prototype.reset=function(){return d[this.size]};var a=0;var r=1;var l=2;var s=3;var p=4;var c=5;var n=6;var o=7;var g=["displaystyle textstyle","textstyle","scriptstyle","scriptscriptstyle"];var d=["reset-textstyle","reset-textstyle","reset-scriptstyle","reset-scriptscriptstyle"];var w=[new h(a,0,1,false),new h(r,0,1,true),new h(l,1,1,false),new h(s,1,1,true),new h(p,2,.7,false),new h(c,2,.7,true),new h(n,3,.5,false),new h(o,3,.5,true)];var u=[p,c,p,c,n,o,n,o];var k=[c,c,c,c,o,o,o,o];var m=[l,s,p,c,n,o,n,o];var f=[s,s,c,c,o,o,o,o];var v=[r,r,s,s,c,c,o,o];t.exports={DISPLAY:w[a],TEXT:w[l],SCRIPT:w[p],SCRIPTSCRIPT:w[n]}},{}],9:[function(e,t,i){var h=e("./domTree");var a=e("./fontMetrics");var r=e("./symbols");var l=e("./utils");var s=["\\Gamma","\\Delta","\\Theta","\\Lambda","\\Xi","\\Pi","\\Sigma","\\Upsilon","\\Phi","\\Psi","\\Omega"];var p=["\u0131","\u0237"];var c=function(e,t,i,l,s){if(r[i][e]&&r[i][e].replace){e=r[i][e].replace}var p=a.getCharacterMetrics(e,t);var c;if(p){c=new h.symbolNode(e,p.height,p.depth,p.italic,p.skew,s)}else{typeof console!=="undefined"&&console.warn("No character metrics for '"+e+"' in style '"+t+"'");c=new h.symbolNode(e,0,0,0,0,s)}if(l){c.style.color=l}return c};var n=function(e,t,i,h){if(e==="\\"||r[t][e].font==="main"){return c(e,"Main-Regular",t,i,h)}else{return c(e,"AMS-Regular",t,i,h.concat(["amsrm"]))}};var o=function(e,t,i,h,a){if(a==="mathord"){return g(e,t,i,h)}else if(a==="textord"){return c(e,"Main-Regular",t,i,h.concat(["mathrm"]))}else{throw new Error("unexpected type: "+a+" in mathDefault")}};var g=function(e,t,i,h){if(/[0-9]/.test(e.charAt(0))||l.contains(p,e)||l.contains(s,e)){return c(e,"Main-Italic",t,i,h.concat(["mainit"]))}else{return c(e,"Math-Italic",t,i,h.concat(["mathit"]))}};var d=function(e,t,i){var h=e.mode;var s=e.value;if(r[h][s]&&r[h][s].replace){s=r[h][s].replace}var n=["mord"];var d=t.getColor();var w=t.font;if(w){if(w==="mathit"||l.contains(p,s)){return g(s,h,d,n)}else{var u=x[w].fontName;if(a.getCharacterMetrics(s,u)){return c(s,u,h,d,n.concat([w]))}else{return o(s,h,d,n,i)}}}else{return o(s,h,d,n,i)}};var w=function(e){var t=0;var i=0;var h=0;if(e.children){for(var a=0;a<e.children.length;a++){if(e.children[a].height>t){t=e.children[a].height}if(e.children[a].depth>i){i=e.children[a].depth}if(e.children[a].maxFontSize>h){h=e.children[a].maxFontSize}}}e.height=t;e.depth=i;e.maxFontSize=h};var u=function(e,t,i){var a=new h.span(e,t);w(a);if(i){a.style.color=i}return a};var k=function(e){var t=new h.documentFragment(e);w(t);return t};var m=function(e,t){var i=u([],[new h.symbolNode("\u200b")]);i.style.fontSize=t/e.style.sizeMultiplier+"em";var a=u(["fontsize-ensurer","reset-"+e.size,"size5"],[i]);return a};var f=function(e,t,i,a){var r;var l;var s;if(t==="individualShift"){var p=e;e=[p[0]];r=-p[0].shift-p[0].elem.depth;l=r;for(s=1;s<p.length;s++){var c=-p[s].shift-l-p[s].elem.depth;var n=c-(p[s-1].elem.height+p[s-1].elem.depth);l=l+c;e.push({type:"kern",size:n});e.push(p[s])}}else if(t==="top"){var o=i;for(s=0;s<e.length;s++){if(e[s].type==="kern"){o-=e[s].size}else{o-=e[s].elem.height+e[s].elem.depth}}r=o}else if(t==="bottom"){r=-i}else if(t==="shift"){r=-e[0].elem.depth-i}else if(t==="firstBaseline"){r=-e[0].elem.depth}else{r=0}var g=0;for(s=0;s<e.length;s++){if(e[s].type==="elem"){g=Math.max(g,e[s].elem.maxFontSize)}}var d=m(a,g);var w=[];l=r;for(s=0;s<e.length;s++){if(e[s].type==="kern"){l+=e[s].size}else{var k=e[s].elem;var f=-k.depth-l;l+=k.height+k.depth;var v=u([],[d,k]);v.height-=f;v.depth+=f;v.style.top=f+"em";w.push(v)}}var y=u(["baseline-fix"],[d,new h.symbolNode("\u200b")]);w.push(y);var x=u(["vlist"],w);x.height=Math.max(l,x.height);x.depth=Math.max(-r,x.depth);return x};var v={size1:.5,size2:.7,size3:.8,size4:.9,size5:1,size6:1.2,size7:1.44,size8:1.73,size9:2.07,size10:2.49};var y={"\\qquad":{size:"2em",className:"qquad"},"\\quad":{size:"1em",className:"quad"},"\\enspace":{size:"0.5em",className:"enspace"},"\\;":{size:"0.277778em",className:"thickspace"},"\\:":{size:"0.22222em",className:"mediumspace"},"\\,":{size:"0.16667em",className:"thinspace"},"\\!":{size:"-0.16667em",className:"negativethinspace"}};var x={mathbf:{variant:"bold",fontName:"Main-Bold"},mathrm:{variant:"normal",fontName:"Main-Regular"},mathbb:{variant:"double-struck",fontName:"AMS-Regular"},mathcal:{variant:"script",fontName:"Caligraphic-Regular"},mathfrak:{variant:"fraktur",fontName:"Fraktur-Regular"},mathscr:{variant:"script",fontName:"Script-Regular"},mathsf:{variant:"sans-serif",fontName:"SansSerif-Regular"},mathtt:{variant:"monospace",fontName:"Typewriter-Regular"}};t.exports={fontMap:x,makeSymbol:c,mathsym:n,makeSpan:u,makeFragment:k,makeVList:f,makeOrd:d,sizingMultiplier:v,spacingFunctions:y}},{"./domTree":14,"./fontMetrics":16,"./symbols":22,"./utils":23}],10:[function(e,t,i){var h=e("./ParseError");var a=e("./Style");var r=e("./buildCommon");var l=e("./delimiter");var s=e("./domTree");var p=e("./fontMetrics");var c=e("./utils");var n=r.makeSpan;var o=function(e,t,i){var h=[];for(var a=0;a<e.length;a++){var r=e[a];h.push(v(r,t,i));i=r}return h};var g={mathord:"mord",textord:"mord",bin:"mbin",rel:"mrel",text:"mord",open:"mopen",close:"mclose",inner:"minner",genfrac:"mord",array:"mord",spacing:"mord",punct:"mpunct",ordgroup:"mord",op:"mop",katex:"mord",overline:"mord",rule:"mord",leftright:"minner",sqrt:"mord",accent:"mord"};var d=function(e){if(e==null){return g.mathord}else if(e.type==="supsub"){return d(e.value.base)}else if(e.type==="llap"||e.type==="rlap"){return d(e.value)}else if(e.type==="color"){return d(e.value.value)}else if(e.type==="sizing"){return d(e.value.value)}else if(e.type==="styling"){return d(e.value.value)}else if(e.type==="delimsizing"){return g[e.value.delimType]}else{return g[e.type]}};var w=function(e,t){if(!e){return false}else if(e.type==="op"){return e.value.limits&&(t.style.size===a.DISPLAY.size||e.value.alwaysHandleSupSub)}else if(e.type==="accent"){return k(e.value.base)}else{return null}};var u=function(e){if(!e){return false}else if(e.type==="ordgroup"){if(e.value.length===1){return u(e.value[0])}else{return e}}else if(e.type==="color"){if(e.value.value.length===1){return u(e.value.value[0])}else{return e}}else{return e}};var k=function(e){var t=u(e);return t.type==="mathord"||t.type==="textord"||t.type==="bin"||t.type==="rel"||t.type==="inner"||t.type==="open"||t.type==="close"||t.type==="punct"};var m=function(e){return n(["sizing","reset-"+e.size,"size5",e.style.reset(),a.TEXT.cls(),"nulldelimiter"])};var f={mathord:function(e,t,i){return r.makeOrd(e,t,"mathord")},textord:function(e,t,i){return r.makeOrd(e,t,"textord")},bin:function(e,t,i){var h="mbin";var a=i;while(a&&a.type==="color"){var l=a.value.value;a=l[l.length-1]}if(!i||c.contains(["mbin","mopen","mrel","mop","mpunct"],d(a))){e.type="textord";h="mord"}return r.mathsym(e.value,e.mode,t.getColor(),[h])},rel:function(e,t,i){return r.mathsym(e.value,e.mode,t.getColor(),["mrel"])},open:function(e,t,i){return r.mathsym(e.value,e.mode,t.getColor(),["mopen"])},close:function(e,t,i){return 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c=n([t.style.reset(),a.TEXT.cls(),"sqrt-line"],[],t.getColor());c.height=s;c.maxFontSize=1;var o=s;if(t.style.id<a.TEXT.id){o=p.metrics.xHeight}var g=s+o/4;var d=(h.height+h.depth)*t.style.sizeMultiplier;var w=d+g+s;var u=n(["sqrt-sign"],[l.customSizedDelim("\\surd",w,false,t,e.mode)],t.getColor());var k=u.height+u.depth-s;if(k>h.height+h.depth+g){g=(g+k-h.height-h.depth)/2}var m=-(h.height+g+s)+u.height;u.style.top=m+"em";u.height-=m;u.depth+=m;var f;if(h.height===0&&h.depth===0){f=n()}else{f=r.makeVList([{type:"elem",elem:h},{type:"kern",size:g},{type:"elem",elem:c},{type:"kern",size:s}],"firstBaseline",null,t)}if(!e.value.index){return n(["sqrt","mord"],[u,f])}else{var y=v(e.value.index,t.withStyle(a.SCRIPTSCRIPT));var x=n([t.style.reset(),a.SCRIPTSCRIPT.cls()],[y]);var b=Math.max(u.height,f.height);var z=Math.max(u.depth,f.depth);var S=.6*(b-z);var M=r.makeVList([{type:"elem",elem:x}],"shift",-S,t);var q=n(["root"],[M]);return n(["sqrt","mord"],[q,u,f])}},sizing:function(e,t,i){var 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a=0;if(e.value.shift){a=e.value.shift.number;if(e.value.shift.unit==="ex"){a*=p.metrics.xHeight}}var r=e.value.width.number;if(e.value.width.unit==="ex"){r*=p.metrics.xHeight}var l=e.value.height.number;if(e.value.height.unit==="ex"){l*=p.metrics.xHeight}a/=t.style.sizeMultiplier;r/=t.style.sizeMultiplier;l/=t.style.sizeMultiplier;h.style.borderRightWidth=r+"em";h.style.borderTopWidth=l+"em";h.style.bottom=a+"em";h.width=r;h.height=l+a;h.depth=-a;return h},accent:function(e,t,i){var h=e.value.base;var a;if(e.type==="supsub"){var l=e;e=l.value.base;h=e.value.base;l.value.base=h;a=v(l,t.reset(),i)}var s=v(h,t.withStyle(t.style.cramp()));var c;if(k(h)){var o=u(h);var g=v(o,t.withStyle(t.style.cramp()));c=g.skew}else{c=0}var d=Math.min(s.height,p.metrics.xHeight);var w=r.makeSymbol(e.value.accent,"Main-Regular","math",t.getColor());w.italic=0;var m=e.value.accent==="\\vec"?"accent-vec":null;var 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r=n(["strut","bottom"]);a.style.height=h.height+"em";r.style.height=h.height+h.depth+"em";r.style.verticalAlign=-h.depth+"em";var l=n(["katex-html"],[a,r,h]);l.setAttribute("aria-hidden","true");return l};t.exports=y},{"./ParseError":5,"./Style":8,"./buildCommon":9,"./delimiter":13,"./domTree":14,"./fontMetrics":16,"./utils":23}],11:[function(e,t,i){var h=e("./buildCommon");var a=e("./fontMetrics");var r=e("./mathMLTree");var l=e("./ParseError");var s=e("./symbols");var p=e("./utils");var c=h.makeSpan;var n=h.fontMap;var o=function(e,t){if(s[t][e]&&s[t][e].replace){e=s[t][e].replace}return new r.TextNode(e)};var g=function(e,t){var i=t.font;if(!i){return null}var h=e.mode;if(i==="mathit"){return"italic"}var r=e.value;if(p.contains(["\\imath","\\jmath"],r)){return null}if(s[h][r]&&s[h][r].replace){r=s[h][r].replace}var l=n[i].fontName;if(a.getCharacterMetrics(r,l)){return n[t.font].variant}return null};var d={mathord:function(e,t){var i=new r.MathNode("mi",[o(e.value,e.mode)]);var 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r.MathNode("mtr",e.map(function(e){return new r.MathNode("mtd",[u(e,t)])}))}))},sqrt:function(e,t){var i;if(e.value.index){i=new r.MathNode("mroot",[u(e.value.body,t),u(e.value.index,t)])}else{i=new r.MathNode("msqrt",[u(e.value.body,t)])}return i},leftright:function(e,t){var i=w(e.value.body,t);if(e.value.left!=="."){var h=new r.MathNode("mo",[o(e.value.left,e.mode)]);h.setAttribute("fence","true");i.unshift(h)}if(e.value.right!=="."){var a=new r.MathNode("mo",[o(e.value.right,e.mode)]);a.setAttribute("fence","true");i.push(a)}var l=new r.MathNode("mrow",i);return l},accent:function(e,t){var i=new r.MathNode("mo",[o(e.value.accent,e.mode)]);var h=new r.MathNode("mover",[u(e.value.base,t),i]);h.setAttribute("accent","true");return h},spacing:function(e){var t;if(e.value==="\\ "||e.value==="\\space"||e.value===" "||e.value==="~"){t=new r.MathNode("mtext",[new r.TextNode("\xa0")])}else{t=new r.MathNode("mspace");t.setAttribute("width",h.spacingFunctions[e.value].size)}return t},op:function(e){var t;if(e.value.symbol){t=new r.MathNode("mo",[o(e.value.body,e.mode)])}else{t=new r.MathNode("mi",[new r.TextNode(e.value.body.slice(1))])}return t},katex:function(e){var t=new r.MathNode("mtext",[new r.TextNode("KaTeX")]);return t},font:function(e,t){var i=e.value.font;return u(e.value.body,t.withFont(i))},delimsizing:function(e){var t=[];if(e.value.value!=="."){t.push(o(e.value.value,e.mode))}var i=new r.MathNode("mo",t);if(e.value.delimType==="open"||e.value.delimType==="close"){i.setAttribute("fence","true")}else{i.setAttribute("fence","false")}return i},styling:function(e,t){var i=w(e.value.value,t);var h=new r.MathNode("mstyle",i);var a={display:["0","true"],text:["0","false"],script:["1","false"],scriptscript:["2","false"]};var l=a[e.value.style];h.setAttribute("scriptlevel",l[0]);h.setAttribute("displaystyle",l[1]);return h},sizing:function(e,t){var i=w(e.value.value,t);var a=new r.MathNode("mstyle",i);a.setAttribute("mathsize",h.sizingMultiplier[e.value.size]+"em");return a},overline:function(e,t){var i=new r.MathNode("mo",[new r.TextNode("\u203e")]);i.setAttribute("stretchy","true");var h=new r.MathNode("mover",[u(e.value.body,t),i]);h.setAttribute("accent","true");return h},rule:function(e){var t=new r.MathNode("mrow");return t},llap:function(e,t){var i=new r.MathNode("mpadded",[u(e.value.body,t)]);i.setAttribute("lspace","-1width");i.setAttribute("width","0px");return i},rlap:function(e,t){var i=new r.MathNode("mpadded",[u(e.value.body,t)]);i.setAttribute("width","0px");return i},phantom:function(e,t,i){var h=w(e.value.value,t);return new r.MathNode("mphantom",h)}};var w=function(e,t){var i=[];for(var h=0;h<e.length;h++){var a=e[h];i.push(u(a,t))}return i};var u=function(e,t){if(!e){return new r.MathNode("mrow")}if(d[e.type]){return d[e.type](e,t)}else{throw new l("Got group of unknown type: '"+e.type+"'")}};var k=function(e,t,i){var h=w(e,i);var a=new r.MathNode("mrow",h);var l=new r.MathNode("annotation",[new r.TextNode(t)]);l.setAttribute("encoding","application/x-tex");var s=new r.MathNode("semantics",[a,l]);var p=new r.MathNode("math",[s]);return c(["katex-mathml"],[p])};t.exports=k},{"./ParseError":5,"./buildCommon":9,"./fontMetrics":16,"./mathMLTree":19,"./symbols":22,"./utils":23}],12:[function(e,t,i){var h=e("./buildHTML");var a=e("./buildMathML");var r=e("./buildCommon");var l=e("./Options");var s=e("./Settings");var p=e("./Style");var c=r.makeSpan;var n=function(e,t,i){i=i||new s({});var r=p.TEXT;if(i.displayMode){r=p.DISPLAY}var n=new l({style:r,size:"size5"});var o=a(e,t,n);var g=h(e,n);var d=c(["katex"],[o,g]);if(i.displayMode){return c(["katex-display"],[d])}else{return d}};t.exports=n},{"./Options":4,"./Settings":7,"./Style":8,"./buildCommon":9,"./buildHTML":10,"./buildMathML":11}],13:[function(e,t,i){var h=e("./ParseError");var a=e("./Style");var r=e("./buildCommon");var l=e("./fontMetrics");var s=e("./symbols");var p=e("./utils");var c=r.makeSpan;var n=function(e,t){if(s.math[e]&&s.math[e].replace){return l.getCharacterMetrics(s.math[e].replace,t)}else{return l.getCharacterMetrics(e,t)}};var o=function(e,t,i){return r.makeSymbol(e,"Size"+t+"-Regular",i)};var g=function(e,t,i){var h=c(["style-wrap",i.style.reset(),t.cls()],[e]);var a=t.sizeMultiplier/i.style.sizeMultiplier;h.height*=a;h.depth*=a;h.maxFontSize=t.sizeMultiplier;return h};var d=function(e,t,i,h,a){var s=r.makeSymbol(e,"Main-Regular",a);var p=g(s,t,h);if(i){var c=(1-h.style.sizeMultiplier/t.sizeMultiplier)*l.metrics.axisHeight;p.style.top=c+"em";p.height-=c;p.depth+=c}return p};var w=function(e,t,i,h,r){var s=o(e,t,r);var p=g(c(["delimsizing","size"+t],[s],h.getColor()),a.TEXT,h);if(i){var n=(1-h.style.sizeMultiplier)*l.metrics.axisHeight;p.style.top=n+"em";p.height-=n;p.depth+=n}return p};var u=function(e,t,i){var h;if(t==="Size1-Regular"){h="delim-size1"}else if(t==="Size4-Regular"){h="delim-size4"}var a=c(["delimsizinginner",h],[c([],[r.makeSymbol(e,t,i)])]);return{type:"elem",elem:a}};var k=function(e,t,i,h,s){var p,o,d,w;p=d=w=e;o=null;var k="Size1-Regular";if(e==="\\uparrow"){d=w="\u23d0"}else if(e==="\\Uparrow"){d=w="\u2016"}else if(e==="\\downarrow"){p=d="\u23d0"}else if(e==="\\Downarrow"){p=d="\u2016"}else if(e==="\\updownarrow"){p="\\uparrow";d="\u23d0";w="\\downarrow"}else if(e==="\\Updownarrow"){p="\\Uparrow";d="\u2016";w="\\Downarrow"}else if(e==="["||e==="\\lbrack"){p="\u23a1";d="\u23a2";w="\u23a3";k="Size4-Regular"}else if(e==="]"||e==="\\rbrack"){p="\u23a4";d="\u23a5";w="\u23a6";k="Size4-Regular"}else if(e==="\\lfloor"){d=p="\u23a2";w="\u23a3";k="Size4-Regular"}else if(e==="\\lceil"){p="\u23a1";d=w="\u23a2";k="Size4-Regular"}else if(e==="\\rfloor"){d=p="\u23a5";w="\u23a6";k="Size4-Regular"}else if(e==="\\rceil"){p="\u23a4";d=w="\u23a5";k="Size4-Regular"}else if(e==="("){p="\u239b";d="\u239c";w="\u239d";k="Size4-Regular"}else 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E;if(o===null){for(E=0;E<A;E++){R.push(u(d,k,s))}}else{for(E=0;E<A;E++){R.push(u(d,k,s))}R.push(u(o,k,s));for(E=0;E<A;E++){R.push(u(d,k,s))}}R.push(u(p,k,s));var P=r.makeVList(R,"bottom",C,h);return g(c(["delimsizing","mult"],[P],h.getColor()),a.TEXT,h)};var m=["(",")","[","\\lbrack","]","\\rbrack","\\{","\\lbrace","\\}","\\rbrace","\\lfloor","\\rfloor","\\lceil","\\rceil","\\surd"];var f=["\\uparrow","\\downarrow","\\updownarrow","\\Uparrow","\\Downarrow","\\Updownarrow","|","\\|","\\vert","\\Vert","\\lvert","\\rvert","\\lVert","\\rVert","\\lgroup","\\rgroup","\\lmoustache","\\rmoustache"];var v=["<",">","\\langle","\\rangle","/","\\backslash"];var y=[0,1.2,1.8,2.4,3];var x=function(e,t,i,a){if(e==="<"){e="\\langle"}else if(e===">"){e="\\rangle"}if(p.contains(m,e)||p.contains(v,e)){return w(e,t,false,i,a)}else if(p.contains(f,e)){return k(e,y[t],false,i,a)}else{throw new h("Illegal delimiter: '"+e+"'")}};var b=[{type:"small",style:a.SCRIPTSCRIPT},{type:"small",style:a.SCRIPT},{type:"small",style:a.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4}];var z=[{type:"small",style:a.SCRIPTSCRIPT},{type:"small",style:a.SCRIPT},{type:"small",style:a.TEXT},{type:"stack"}];var S=[{type:"small",style:a.SCRIPTSCRIPT},{type:"small",style:a.SCRIPT},{type:"small",style:a.TEXT},{type:"large",size:1},{type:"large",size:2},{type:"large",size:3},{type:"large",size:4},{type:"stack"}];var M=function(e){if(e.type==="small"){return"Main-Regular"}else if(e.type==="large"){return"Size"+e.size+"-Regular"}else if(e.type==="stack"){return"Size4-Regular"}};var q=function(e,t,i,h){var a=Math.min(2,3-h.style.size);for(var r=a;r<i.length;r++){if(i[r].type==="stack"){break}var l=n(e,M(i[r]));var s=l.height+l.depth;if(i[r].type==="small"){s*=i[r].style.sizeMultiplier}if(s>t){return i[r]}}return i[i.length-1]};var A=function(e,t,i,h,a){if(e==="<"){e="\\langle"}else if(e===">"){e="\\rangle"}var r;if(p.contains(v,e)){r=b}else if(p.contains(m,e)){r=S}else{r=z}var l=q(e,t,r,h);if(l.type==="small"){return d(e,l.style,i,h,a)}else if(l.type==="large"){return w(e,l.size,i,h,a)}else if(l.type==="stack"){return k(e,t,i,h,a)}};var T=function(e,t,i,h,a){var r=l.metrics.axisHeight*h.style.sizeMultiplier;var s=901;var p=5/l.metrics.ptPerEm;var c=Math.max(t-r,i+r);var n=Math.max(c/500*s,2*c-p);return A(e,n,true,h,a)};t.exports={sizedDelim:x,customSizedDelim:A,leftRightDelim:T}},{"./ParseError":5,"./Style":8,"./buildCommon":9,"./fontMetrics":16,"./symbols":22,"./utils":23}],14:[function(e,t,i){var h=e("./utils");var a=function(e){e=e.slice();for(var t=e.length-1;t>=0;t--){if(!e[t]){e.splice(t,1)}}return e.join(" ")};function r(e,t,i,h,a,r){this.classes=e||[];this.children=t||[];this.height=i||0;this.depth=h||0;this.maxFontSize=a||0;this.style=r||{};this.attributes={}}r.prototype.setAttribute=function(e,t){this.attributes[e]=t};r.prototype.toNode=function(){var e=document.createElement("span");e.className=a(this.classes);for(var t in this.style){if(Object.prototype.hasOwnProperty.call(this.style,t)){e.style[t]=this.style[t]}}for(var i in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,i)){e.setAttribute(i,this.attributes[i])}}for(var h=0;h<this.children.length;h++){e.appendChild(this.children[h].toNode())}return e};r.prototype.toMarkup=function(){var e="<span";if(this.classes.length){e+=' class="';e+=h.escape(a(this.classes));e+='"'}var t="";for(var i in this.style){if(this.style.hasOwnProperty(i)){t+=h.hyphenate(i)+":"+this.style[i]+";"}}if(t){e+=' style="'+h.escape(t)+'"'}for(var r in this.attributes){if(Object.prototype.hasOwnProperty.call(this.attributes,r)){e+=" "+r+'="';e+=h.escape(this.attributes[r]);e+='"'}}e+=">";for(var l=0;l<this.children.length;l++){e+=this.children[l].toMarkup()}e+="</span>";return e};function l(e,t,i,h){this.children=e||[];this.height=t||0;this.depth=i||0;this.maxFontSize=h||0}l.prototype.toNode=function(){var e=document.createDocumentFragment();for(var t=0;t<this.children.length;t++){e.appendChild(this.children[t].toNode())}return e};l.prototype.toMarkup=function(){var e="";for(var t=0;t<this.children.length;t++){e+=this.children[t].toMarkup()}return e};function s(e,t,i,h,a,r,l){this.value=e||"";this.height=t||0;this.depth=i||0;this.italic=h||0;this.skew=a||0;this.classes=r||[];this.style=l||{};this.maxFontSize=0}s.prototype.toNode=function(){var e=document.createTextNode(this.value);var t=null;if(this.italic>0){t=document.createElement("span");t.style.marginRight=this.italic+"em"}if(this.classes.length>0){t=t||document.createElement("span");t.className=a(this.classes)}for(var i in this.style){if(this.style.hasOwnProperty(i)){t=t||document.createElement("span");t.style[i]=this.style[i]}}if(t){t.appendChild(e);return t}else{return e}};s.prototype.toMarkup=function(){var e=false;var t="<span";if(this.classes.length){e=true;t+=' class="';t+=h.escape(a(this.classes));t+='"'}var i="";if(this.italic>0){i+="margin-right:"+this.italic+"em;"}for(var r in this.style){if(this.style.hasOwnProperty(r)){i+=h.hyphenate(r)+":"+this.style[r]+";"}}if(i){e=true;t+=' style="'+h.escape(i)+'"'}var l=h.escape(this.value);if(e){t+=">";t+=l;t+="</span>";return t}else{return l}};t.exports={span:r,documentFragment:l,symbolNode:s}},{"./utils":23}],15:[function(e,t,i){var h=e("./fontMetrics");var a=e("./parseData");var r=e("./ParseError");var l=a.ParseNode;var s=a.ParseResult;function p(e,t,i,h){var a=[],p=[a],c=[];while(true){var n=e.parseExpression(t,i,false,null);a.push(new l("ordgroup",n.result,i));t=n.position;var o=n.peek.text;if(o==="&"){t=n.peek.position}else if(o==="\\end"){break}else if(o==="\\\\"||o==="\\cr"){var g=e.parseFunction(t,i);c.push(g.result.value.size);t=g.position;a=[];p.push(a)}else{throw new r("Expected & or \\\\ or 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":{font:"main",group:"spacing",replace:"\xa0"}," ":{font:"main",group:"spacing",replace:"\xa0"},"~":{font:"main",group:"spacing",replace:"\xa0"}}};var a='0123456789/@."';for(var r=0;r<a.length;r++){var l=a.charAt(r);h.math[l]={font:"main",group:"textord"}}var s="0123456789`!@*()-=+[]'\";:?/.,";for(var r=0;r<s.length;r++){var l=s.charAt(r);h.text[l]={font:"main",group:"textord"}}var p="abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";for(var r=0;r<p.length;r++){var l=p.charAt(r);h.math[l]={font:"main",group:"mathord"};h.text[l]={font:"main",group:"textord"}}t.exports=h},{}],23:[function(e,t,i){var h=Array.prototype.indexOf;var a=function(e,t){if(e==null){return-1}if(h&&e.indexOf===h){return e.indexOf(t)}var i=0,a=e.length;for(;i<a;i++){if(e[i]===t){return i}}return-1};var r=function(e,t){return a(e,t)!==-1};var l=function(e,t){return e===undefined?t:e};var s=/([A-Z])/g;var p=function(e){return e.replace(s,"-$1").toLowerCase()};var c={"&":"&amp;",">":"&gt;","<":"&lt;",'"':"&quot;","'":"&#x27;"};var n=/[&><"']/g;function o(e){return c[e]}function g(e){return(""+e).replace(n,o)}var d;if(typeof document!=="undefined"){var w=document.createElement("span");if("textContent"in w){d=function(e,t){e.textContent=t}}else{d=function(e,t){e.innerText=t}}}function u(e){d(e,"")}t.exports={contains:r,deflt:l,escape:g,hyphenate:p,indexOf:a,setTextContent:d,clearNode:u}},{}]},{},[1])(1)});

main.css

html, body {
  width: 100%;
  height: 100%;
  margin: 0;
  padding: 0;
  font-family: sans-serif;
}

.container {
  width: 100%;
  height: 100%;
}

.instructions {
  position: relative;
  z-index: 3;
  padding: 1em;
  font-style: italic;
  text-align: center;
  pointer-events: none;
  font-size: 10px;
}

svg {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;  
  z-index: 2;
}

canvas {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;
  z-index: 1;
}

line {
  stroke: black;
}

rect.click-capture {
  pointer-events: all;
  visibility: hidden;
  cursor: pointer;
}


g.relationship {
  pointer-events: none;
}
g.relationship path {
  stroke: #ccc;
}
g.relationship text.prose {
  font-size: 12px;
  text-anchor: middle;
}
g.relationship text.prose {
  font-size: 10px;
}

g.parameter-control rect.frame {
  stroke: black;
  stroke-width: 1;
  fill: rgba(255,255,255,.5);
  cursor: crosshair;
}
g.parameter-control path.axis {
  stroke: #ddd;
}

g.parameter-control text {
  text-anchor: middle;
  font-size: 8px;
  fill: #ccc;
  pointer-events: none;
}
g.parameter-control text.title {
  fill: #000;
  font-weight: bold;
}
g.parameter-control text.prose {
  fill: #000;
}

div.heart {
  position: absolute;
  z-index: 3;
  transform: translate(-50%,-50%);
}

.symbolics {
  position: absolute;
  z-index: 3;
  bottom: 20px;
  left: 50%;
  transform: translate(-50%,0);
  background: rgba(255,255,255,.5);
  pointer-events: none;
}
.symbolics .eq {
  padding: .5em 0;
}

main.js

'use strict';

var hearts = ['💞','💖','💓','💜','💘'];
var randHeart = function() {
  return hearts[Math.floor(Math.random() * hearts.length)];
}

// var maxParam = .03;
var maxParam = .01;
var randParam = function() {
  return d3.scale.linear().range([-maxParam,maxParam])(Math.random());
}

var line = d3.svg.line();

var container = d3.select('.container');

var svg = container.append("svg"),
    width = container.node().offsetWidth,
    height = container.node().offsetHeight,
    minDim = Math.min(width,height);

var feelingScale = d3.scale.quantize()
  .domain([-minDim/4,-minDim/8,0,minDim/8,minDim/4])
  .range(['hates','dislikes','is ok with','likes','loves']);

var feelingScaleEmoji = d3.scale.quantize()
  .domain([-minDim/4,-minDim/8,0,minDim/8,minDim/4])
  .range(['😩','😔','😐','😊','😍']);

var canvas = container.append("canvas")
  .attr("width", width)
  .attr("height", height);
var ctx = canvas.node().getContext('2d');
ctx.translate(width/2,height/2);
ctx.fillStyle = '#eee';

var g = svg.append("g")
  .attr("transform", "translate(" + width/2 + "," + height/2 + ")");

var yAxis = g.append("line")
  .attr('class', 'y axis')
  .attr('x1', 0)
  .attr('x2', 0)
  .attr('y1', -height/2)
  .attr('y2', height/2);

var xAxis = g.append("line")
  .attr('class', 'x axis')
  .attr('x1', -width/2)
  .attr('x2', width/2)
  .attr('y1', 0)
  .attr('y2', 0);

var clickCapture = g.append('rect')
  .attr('class', 'click-capture')
  .attr('x', -width/2)
  .attr('y', -height/2)
  .attr('height', height)
  .attr('width', width);

var relationship = {
  'x': {
    'dim': 'x',
    'name': 'Romeo',
    'value': Math.random() * width - width/2,
    'coefficients': {
      'x': randParam(),
      'y': randParam()
    }
  },
  'y': {
    'dim': 'y',
    'name': 'Juliet',
    'value': Math.random() * height - height/2,
    'coefficients': {
      'x': randParam(),
      'y': randParam()
    }
  }
};

var lesserRelationships = d3.range(20).map(newPoint);

var point = g.append("g")
  .attr("class", "relationship")
  .datum(relationship)

point.append("path").attr("class", "x");
point.append("path").attr("class", "y");
point.append("circle").attr("r", "4");
point.append("text").attr("class", "face x").attr("dy", ".3em").attr("dx", "-.5em");
point.append("text").attr("class", "face y").attr("dy", ".3em").attr("dx", "-.5em");
point.append("text").attr("class", "prose x").attr("dy", ".3em").style('text-anchor', 'middle');
point.append("text").attr("class", "prose y").attr("dy", ".3em").attr("dx", "-.5em")

g.on("click", function() {

  // remove instruction to do this
  d3.select('.instructions .main')
    .remove();

  var x = d3.mouse(this)[0]
  var y = -d3.mouse(this)[1]
  relationship.x.value = x;
  relationship.y.value = y;
})

d3.select('.symbolics')
  .datum(relationship)
  .call(renderSymbolics);

svg.selectAll('g.parameter-control')
  .data(Object.keys(relationship))
  .enter()
  .append('g')
  .attr('class', 'parameter-control')
  .attr("transform", function(d,i) {
    if(i==0) {
      return "translate(" + 25 + "," + (height-125) + ")"
    } else {
      return "translate(" + (width-125) + "," + (height-125) + ")"
    }
  })
  .call(controlBox);

var lastHearted = 0;
var lastHeartedInterval = 100;
d3.timer(function(t) {

  point
    .each(function(d) {

      // if it goes too far offscreen, reset
      if(Math.abs(d.x.value) > width * 2 && Math.abs(d.y.value) > height * 2) {
        d.x.value = Math.random() * width - width/2;
        d.y.value = Math.random() * height - height/2;
      }

      // calculate one tick in the sim
      var dims = Object.keys(relationship);
      dims.forEach(function(dim) {
        dims.forEach(function(dim2) {
          d[dim].value += d[dim].coefficients[dim2] * d[dim2].value;
        });
      });

      // leave trail
      ctx.beginPath();
      ctx.arc(d.x.value,-d.y.value,4,0,2*Math.PI);
      ctx.fill();

      // spew hearts if you're in love <3
      if(feelingScale(d.x.value)=='loves' && feelingScale(d.y.value)=='loves') {
        if(t-lastHearted > lastHeartedInterval) {
          container.append('div')
            .attr('class', 'heart')
            .html(randHeart())
            .style('left', (width/2 + d.x.value)+'px')
            .style('top', (height/2 -d.y.value)+'px')
            .style('opacity',1)
            .transition()
            .duration(750)
            .ease('linear')
            .style('left', (width/2 + d.x.value + (Math.random() * 100 - 50))+'px')
            .style('top', (height/2 -d.y.value + (Math.random() * 100 - 50))+'px')
            .style('opacity',0)
            .remove();
          lastHearted = t;
        }
      }

    })
    .attr("transform", function(d) { return "translate("+ d.x.value +","+ -d.y.value +")" });

  // labelings lines and text and emoji
  point.select('path.x').attr('d', function(d) { return line([[0,0],[-d.x.value,0]]); });
  point.select('path.y').attr('d', function(d) { return line([[0,0],[0,d.y.value]]); });
  point.select('text.face.x')
    .attr("x", 0)
    .attr("y", function(d) { return d.y.value; })
    .text(function(d) { return feelingScaleEmoji(d.x.value)});
  point.select('text.face.y')
    .attr("x", function(d) { return -d.x.value; })
    .attr("y", 0)
    .text(function(d) { return feelingScaleEmoji(d.y.value)});
  point.select('text.prose.x')
    .attr("x", 0)
    .attr("y", function(d) { return d.y.value; })
    .attr("dy", function(d) { return 0.3 + (d.y.value > 0 ? 1.2 : -1.2) +'em'; })
    .text(function(d) {
      return 'Romeo ' + feelingScale(d.x.value) + ' Juliet';
    });
  point.select('text.prose.y')
    .attr("x", function(d) { return -d.x.value; })
    .attr("y", 0)
    .style('text-anchor', function(d) { return d.x.value > 0 ? 'end' : 'start'; })
    .attr('dx', function(d) { return (d.x.value < 0 ? 1.2 : -1.2) + 'em'; })
    .text(function(d) {
      return 'Juliet ' + feelingScale(d.y.value) + ' Romeo';
    });

  // draw the faint phase space field lines in the background
  ctx.save();
  ctx.strokeStyle = '#eee';
  lesserRelationships.forEach(function(pt) {

    // if it's gone offscreen, or just 1 in 100 other times (to keep things fresh)
    if(Math.abs(pt.x) > width/2 || Math.abs(pt.y) > height/2 || Math.random() > .99) {
      var newPt = newPoint();
      pt.x = newPt.x;
      pt.y = newPt.y;
      return;
    }

    ctx.beginPath();
    ctx.moveTo(pt.x,-pt.y);

    pt.x += pt.x * relationship.x.coefficients.x + pt.y * relationship.x.coefficients.y;
    pt.y += pt.x * relationship.y.coefficients.x + pt.y * relationship.y.coefficients.y;

    ctx.lineTo(pt.x,-pt.y);
    ctx.stroke();
  });
  ctx.restore();

})

function newPoint() {
  return {
    'x': d3.scale.linear().range([-width/2,width/2])(Math.random()),
    'y': d3.scale.linear().range([-height/2,height/2])(Math.random())
  }
}

// (semi)reusable component for the parameter spaces
function controlBox(selection) {
  selection.each(function(data) {
    var sel = d3.select(this);
    data = relationship[data];

    var w = 100;
    var h = 100;

    // scale clicks to param values
    var mouseToParam = d3.scale.linear()
      .domain([0,w/2])
      .range([0,maxParam]);

    // INITIAL BUILD

    var g = sel.selectAll('g.inner')
      .data([data])
      .enter()
      .append('g')
      .attr("class", "inner")
      .attr("transform", "translate(" + w/2 + "," + h/2 + ")");

    g.append('path').attr("class", "x axis").attr('d', line([[-w/2,0],[w/2,0]]));
    g.append('path').attr("class", "y axis").attr('d', line([[0,-h/2],[0,h/2]]));
    g.append('rect').attr("class", "frame")
      .attr('x', -w/2)
      .attr('y', -h/2)
      .attr('width', w)
      .attr('height', h);

    // label quadrants accd to J. C. Sprott
    // http://sprott.physics.wisc.edu/pubs/paper277.pdf
    g.append('text').attr('x', w/4).attr('y', -h/4).attr('dy', '.3em').text('EAGER')
    g.append('text').attr('x', w/4).attr('y', h/4).attr('dy', '.3em').text('NARCISSIST')
    g.append('text').attr('x', -w/4).attr('y', -h/4).attr('dy', '.3em').text('CAUTIOUS')
    g.append('text').attr('x', -w/4).attr('y', h/4).attr('dy', '.3em').text('HERMIT')

    g.append('text').attr('class', 'title').attr('y',-(h/2 + 10)).text(data.name.toUpperCase());
    g.append('text').attr('class', 'prose one').attr('y', h/2 + 10);
    g.append('text').attr('class', 'prose two').attr('y', h/2 + 20);
    g.append('circle').attr('class', 'current').attr('r', 2);

    var drag = d3.behavior.drag().on('drag', clickOrDrag);
    g.on('click', clickOrDrag).call(drag);

    update();

    function clickOrDrag(d) {

      // remove instruction to do this
      d3.select('.instructions .params').remove();

      // coefficient for own feeling
      var a = mouseToParam(d3.mouse(this)[0]);
      d.coefficients[d.dim] = a;

      // coefficient for other's feeling
      var b = mouseToParam(-d3.mouse(this)[1]);
      d.coefficients[(d.dim==='x' ? 'y' : 'x')] = b;

      update();
    }

    // UPDATE
    function update() {

      var a = data.coefficients[data.dim];
      var b = data.coefficients[(data.dim==='x' ? 'y' : 'x')];

      var hisHer = data.name == 'Romeo' ? 'his' : 'her';
      var heShe = data.name == 'Romeo' ? 'he' : 'she';
      var other = data.name == 'Romeo' ? 'Juliet' : 'Romeo';

      // this text also comes from
      // http://sprott.physics.wisc.edu/pubs/paper277.pdf
      var prose1, prose2;
      if(a > 0 && b > 0) {
        prose1 = 'is encouraged by '+hisHer+' own feelings';
        prose2 = 'as well as '+ other +'’s';
      } else if(a > 0 && b < 0) {
        prose1 = 'wants more of what '+heShe+' feels';
        prose2 = 'but retreats from '+ other +'’s feelings';
      } else if(a < 0 && b > 0) {
        prose1 = 'retreats from '+hisHer+' own feelings';
        prose2 = 'but is encouraged by '+other+'’s';
      } else if(a < 0 && b < 0) {
        prose1 = 'retreats from '+hisHer+' own feelings';
        prose2 = 'as well as '+other+'’s';
      }

      sel.select('circle.current')
        .attr('cx', mouseToParam.invert(a))
        .attr('cy', mouseToParam.invert(-b))

      sel.select('.prose.one').text(prose1);
      sel.select('.prose.two').text(prose2);

      // update symbolic equation
      d3.select('.symbolics').call(renderSymbolics);

      // clear phase space field trails
      ctx.save();
      ctx.fillStyle = '#fff';
      ctx.globalAlpha = .8;
      ctx.fillRect(-width/2,-height/2,width,height);
      ctx.restore();
      // reset seeds for phase space trails
      lesserRelationships = d3.range(20).map(newPoint);

    }

  })
}

// SYMBOLIC REPRESENTATION
// per request by bret victor ;)
// https://twitter.com/worrydream/status/699068236214566915
function renderSymbolics(selection) {
  selection.each(function(data) {
    var sel = d3.select(this);

    var dR = sel.selectAll("div.eq.dR").data([data.x]);
    dR.enter().append("div").attr('class', 'eq dR');

    var dJ = sel.selectAll("div.eq.dJ").data([data.y]);
    dJ.enter().append("div").attr('class', 'eq dJ');

    var a = (data.x.coefficients.x * 1000).toPrecision(3);
    var b = (data.x.coefficients.y * 1000).toPrecision(3);
    katex.render("\\dfrac{dR}{dt} = "+a+"R + "+b+"J", dR.node());

    var c = (data.y.coefficients.x * 1000).toPrecision(3);
    var d = (data.y.coefficients.y * 1000).toPrecision(3);
    katex.render("\\dfrac{dJ}{dt} = "+c+"R + "+d+"J", dJ.node());
  })
}

preview.png

thumbnail.png

todo.md

• Trace-determinant plane
• Lots more lovers
• Transition reparameterization (click and dot quickly transitions to new point, everything shifts)
• Click spawns new couple
• Randomize names
• Use matrices? lol
• Should also try a catastrophe theory model :)

The link to Strogatz's paper 404s, but there's an archived version at https://web.archive.org/web/20050429161901/http://www.stanford.edu/~rajatr/articles/SS_love_dEq.pdf.

This is interesting to know.