making fractal pendant in shapejs - gathering 4 …...vladimir bulatov, shapeways g4g12 march...
TRANSCRIPT
![Page 1: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/1.jpg)
Vladimir Bulatov,
Shapeways
G4G12March 31,2016
Making Fractal Pendant in ShapeJS
![Page 2: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/2.jpg)
Good Old Times
BASIC code for Mandelbrot set fractal2000 REM Initialize the color palette2030 LET L = 1002040 FOR I = 0 TO 1002050 FOR J = 0 TO 1002060 LET U = I / 50 - 1.52070 LET V = J / 50 - 12080 LET X = U2090 LET Y = V2100 LET N = 02120 LET R = X * X2130 LET Q = Y * Y2140 IF R + Q > 4 OR N >= L THEN GOTO 21902150 LET Y = 2 * X * Y + V2160 LET X = R - Q + U2170 LET N = N + 12180 GOTO 21202200 IF N < 10 THEN LET C = "black" ELSE LET C = P[ROUND(8 * (N-10) / (L-10))]2210 PLOT I, J, C 2220 NEXT J2230 NEXT I2240 END
![Page 3: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/3.jpg)
Modern Times
ShapeJS web based IDE
![Page 4: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/4.jpg)
a torus
function main(args) { w = 12*MM; Rout = 5*MM; Rin = 2*MM; bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout); scene = new Scene(shape,bounds); return scene;}
Simple shape
![Page 5: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/5.jpg)
larger torus
function main(args) { w = 12*MM; Rout = 8*MM; Rin = 2*MM; bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout); scene = new Scene(shape,bounds); return scene;}
Simple shape
![Page 6: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/6.jpg)
fatter torus
function main(args) { w = 12*MM; Rout = 5*MM; Rin = 5*MM; bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout); scene = new Scene(shape,bounds); return scene;}
Simple shape
![Page 7: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/7.jpg)
tilted torus
function main(args) { w = 12*MM; Rout = 8*MM; Rin = 2*MM; axis = new Vector3d(-1,0,1); bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout, axis); scene = new Scene(shape,bounds); return scene;}
Simple shape
![Page 8: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/8.jpg)
twisted torus
function main(args) { w = 12*MM; Rout = 8*MM; Rin = 2*MM; axis = new Vector3d(-1,-1,1); bounds = new Bounds(-w,w,-w,w,-w,w); shape = new Torus(Rin, Rout, axis); scene = new Scene(shape,bounds); return scene;}
Not much fun
Simple shape
![Page 9: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/9.jpg)
Torus and mirror
Torus + Mirror
![Page 10: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/10.jpg)
Torus and it's siamese twin
Torus + Mirror
![Page 11: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/11.jpg)
Moving original torus.
It's twin moves in opposite direction
Torus + Mirror
![Page 12: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/12.jpg)
Tilting original torus.
It's twin tilts in opposite direction
Torus + Mirror
![Page 13: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/13.jpg)
Going wild - 2 mirrors
Torus + 2 Mirrors
![Page 14: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/14.jpg)
family of quadruplets
Torus + 2 Mirrors
![Page 15: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/15.jpg)
Motion of original torus moves all siblings
Torus + 2 Mirrors
![Page 16: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/16.jpg)
Changing mirror angle makes larger family
Torus + 2 Mirrors
![Page 17: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/17.jpg)
Changing mirror angle makes larger family
Torus + 2 Mirrors
![Page 18: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/18.jpg)
Changing mirror angle makes larger family
Torus + 2 Mirrors
![Page 19: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/19.jpg)
Moving one family member changes the lookof the whole family
Torus + 2 Mirrors
![Page 20: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/20.jpg)
Moving one family member changes the lookof the whole family
Torus + 2 Mirrors
![Page 21: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/21.jpg)
Going insane!
Using 3 mirrors
Torus + 3 Mirrors
![Page 22: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/22.jpg)
Got infinite family.
But the family is rather orderly and boring
Torus + 3 Mirrors
![Page 23: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/23.jpg)
Got infinite family.
But the family is rather orderly and boring
Very predictable
Torus + 3 Mirrors
![Page 24: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/24.jpg)
Twisting one sibling makes all family do thesame
Torus + 3 Mirrors
![Page 25: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/25.jpg)
Another family made with 3 different mirrors
Torus + 3 Mirrors
![Page 26: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/26.jpg)
Another family made with 3 different mirrors
There are only 3 such families
3, 3, 3
2, 3, 6
2,
4,4
Torus + 3 Mirrors
![Page 27: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/27.jpg)
Can we do better with 4 mirrors?
Torus + 4 Mirrors
![Page 28: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/28.jpg)
4 mirrors
boring
Torus + 4 Mirrors
![Page 29: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/29.jpg)
4 mirrors
boring
BORING
Torus + 4 Mirrors
![Page 30: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/30.jpg)
4 mirrors
boring
BORING
BORING
Torus + 4 Mirrors
![Page 31: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/31.jpg)
4 mirrors
boring
BORING
BORING
BORING
Torus + 4 Mirrors
![Page 32: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/32.jpg)
Magical spherical mirrors!
Spherical Mirrors
![Page 33: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/33.jpg)
Magical spherical mirrors!
Spherical Mirrors
![Page 34: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/34.jpg)
Magical spherical mirrors!
Spherical Mirrors
![Page 35: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/35.jpg)
Reflection in 2 flat mirrors produce familiarresult
Spherical Mirrors
![Page 36: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/36.jpg)
Addition of 3rd spherical mirror givessomething new
Spherical Mirrors
![Page 37: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/37.jpg)
Addition of 3rd spherical mirror givessomething new
Spherical Mirrors
![Page 38: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/38.jpg)
All 4 mirrors make shape with fractal boundary
Spherical Mirrors
![Page 39: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/39.jpg)
Deformation of mirrors arrangement makesnon trivial change of shape
Spherical Mirrors
![Page 40: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/40.jpg)
Deformation of mirrors arrangement makesnon trivial change of shape
Spherical Mirrors
![Page 41: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/41.jpg)
Deformation of mirrors arrangement makesnon trivial change of shape
Spherical Mirrors
![Page 42: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/42.jpg)
Deformation of mirrors arrangement makesnon trivial change of shape
Spherical Mirrors
![Page 43: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/43.jpg)
Deformation of mirrors arrangement makesnon trivial change of shape
Spherical Mirrors
![Page 44: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/44.jpg)
Deformation of mirrors arrangement makesnon trivial change of shape
Spherical Mirrors
![Page 45: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/45.jpg)
The shape is three dimensional
3D view
![Page 46: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/46.jpg)
The shape is three dimensional
3D view
![Page 47: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/47.jpg)
The shape is three dimensional
3D view
![Page 48: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/48.jpg)
The shape is three dimensional
3D view
![Page 49: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/49.jpg)
Samples
![Page 50: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/50.jpg)
Samples
![Page 51: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/51.jpg)
Samples
![Page 52: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/52.jpg)
Samples
![Page 53: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/53.jpg)
Samples
![Page 54: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/54.jpg)
Samples
![Page 55: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/55.jpg)
Samples
![Page 56: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/56.jpg)
Samples
![Page 57: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/57.jpg)
Samples
![Page 58: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/58.jpg)
Samples
![Page 59: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/59.jpg)
Samples
![Page 60: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/60.jpg)
Samples
![Page 61: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/61.jpg)
Samples
![Page 62: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/62.jpg)
Samples
![Page 63: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/63.jpg)
Samples
![Page 64: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/64.jpg)
Samples
![Page 65: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/65.jpg)
Samples
![Page 66: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/66.jpg)
Samples
![Page 67: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/67.jpg)
Samples
![Page 68: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/68.jpg)
Samples
![Page 69: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/69.jpg)
Final choice for pendant
![Page 70: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/70.jpg)
Fractal boundary is too thin to print
It needs to be "thickened"
Geometry of pendant
![Page 71: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/71.jpg)
Fractal boundary is too thin to print
It needs to be "thickened"
Thickening of boundary
![Page 72: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/72.jpg)
Fractal boundary is too thin to print
It needs to be "thickened"
Thickening of boundary
![Page 73: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/73.jpg)
Fractal boundary is too thin to print
It needs to be "thickened"
Thickening of boundary
![Page 74: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/74.jpg)
Fractal boundary is too thin to print
It needs to be "thickened"
Thickening of boundary
![Page 75: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/75.jpg)
3D print needs 3D mesh file
Conversion into Mesh
![Page 76: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/76.jpg)
Bundling 10 pendants in group reducesmaniufacturing cost
Maling a Bundle
![Page 77: Making Fractal Pendant in ShapeJS - Gathering 4 …...Vladimir Bulatov, Shapeways G4G12 March 31,2016 Making Fractal Pendant in ShapeJS Good Old Times BASIC code for Mandelbrot set](https://reader033.vdocuments.net/reader033/viewer/2022041519/5e2d14ee1fc6b84eea400374/html5/thumbnails/77.jpg)
ShapeJS summary
simple to code (javascript)
volumetric modeling via signed distance function
real time server side 3D rendering
compatible with any device which can run web browser
3D print compatible models
easy model sharing
intellectual property protection
We are actively extending the system by adding new capabilities.
Suggestions are very welcome!