Creator of vZome, a free desktop app for modeling Zometool and similar geometries.
Rendering vZome JSON ExportsExploding 4D Star PolytopesThe J92 Rhombochoron in ZomeOmnitruncated HypercubeFive Tetrahedra and Blue-Green ZomeRendering vZome FilesvZome Icosahedral OrbitsA Shape for White StrutsExploring 4D Quaternion RotationsObservable vZome RenderingIcosahedral Symmetry KeysWIP Importing vZome ShapesOrbits of Icosahedral SymmetryWIP Observable vZome
Finding Golden Numbers
replacement = item => (item == "1")? [ "φ" ] : [ "1", "φ" ]
symbolSequence( 7 )
symbolSequence = function( depth ){
function recurrence( arr ){
return arr .reduce( (acc, item) => {
return [ ...acc, ...replacement( item ) ]
}, [] )
}
var seq = [ "1" ]
for (var i = 0; i < depth; i++) {
seq = recurrence( seq )
}
return seq
}
goldenSequence = function( depth ){
return symbolSequence( depth ) .map( symbol => ( ( symbol == "1" )? [1,0,1] : [0,1,1] ) )
}
goldenSequence( 5 )
goldenSequence( 5 ) .map( numberString )
goldenSequence( 5 ) .map( toFixed )
goldenSeries = function( depth ) {
return goldenSequence( depth ) .reduce( function( r, a ) {
if (r.length > 0)
a = gradd( a, r[r.length - 1] );
r .push( a );
return r;
}, [])
}
goldenSeries( 5 ) .map( numberString )
unitGoldenSeries = function( depth ) {
const divisor = grpow( [,1], depth )
return [ [0], ...goldenSeries( depth ) .map( gr => grdiv( gr, divisor ) ) ]
}
unitGoldenSeries( 5 ) .map( numberString )
unitGoldenSeries( 5 ) .map( toFixed )
unitGoldenSlider = function( depth ) {
const values = unitGoldenSeries( depth );
return slider({
value: this ? this.input.value : 0, step: 1, max: values.length - 1,
getValue: n => values[n.value],
display: valueAndString
});
}
findGoldenNumber = function( value, depth )
{
if ( value < 0 )
return null // not yet ready to deal with negatives
if ( value > 1 )
return null
const targets = unitGoldenSeries( depth )
const values = targets .map( grfloat )
function checkRange( minIndex, maxIndex ) {
if ( minIndex >= maxIndex )
// just to be safe, though this should never happen
return targets[ maxIndex ]
else {
const lowDiff = value - values[ minIndex ]
const highDiff = values[ maxIndex ] - value
if ( maxIndex == minIndex + 1 ) {
return ( highDiff < lowDiff )? targets[ maxIndex ] : targets[ minIndex ]
} else {
const midIndex = Math.floor( ( maxIndex + minIndex ) / 2 )
return ( highDiff < lowDiff )? checkRange( midIndex, maxIndex ) : checkRange( minIndex, midIndex )
}
}
}
return checkRange( 0, targets.length -1 )
}
toFixed = v => Number( grfloat( v ) .toPrecision( 7 ) )
valueAndString = v => grfloat( v ) .toFixed( 6 ) + " = " + numberString( v )
import {numberString} from "@vorth/wip-observable-vzome"
import { gradd, grfloat, grdiv, grpow } from '@jrus/zome-arithmetic'
import {slider} from '@jashkenas/inputs'
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