Question

Write a three.js/HTML programming to generate a Sierpenski Triangle using recursion (generate until 10 depth of recursion)

Need the index code with it too so I am able to run it

Example of triangle below:

Answer 1

The Sierpiński triangle (sometimes spelled Sierpinski), is also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle,subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.

code for Sierpiński triangle

import turtle

def drawTriangle(points,color,myTurtle):

    myTurtle.fillcolor(color)

    myTurtle.up()

    myTurtle.goto(points[0][0],points[0][1])

    myTurtle.down()

    myTurtle.begin_fill()

    myTurtle.goto(points[1][0],points[1][1])

    myTurtle.goto(points[2][0],points[2][1])

    myTurtle.goto(points[0][0],points[0][1])

    myTurtle.end_fill()

def getMid(p1,p2):

    return ( (p1[0]+p2[0]) / 2, (p1[1] + p2[1]) / 2)

def sierpinski(points,degree,myTurtle):

    colormap = ['blue','red','green','white','yellow',

                'violet','orange']

    drawTriangle(points,colormap[degree],myTurtle)

    if degree > 0:

        sierpinski([points[0],

                        getMid(points[0], points[1]),

                        getMid(points[0], points[2])],

                   degree-1, myTurtle)

        sierpinski([points[1],

                        getMid(points[0], points[1]),

                        getMid(points[1], points[2])],

                   degree-1, myTurtle)

        sierpinski([points[2],

                        getMid(points[2], points[1]),

                        getMid(points[0], points[2])],

                   degree-1, myTurtle)

def main():

   myTurtle = turtle.Turtle()

   myWin = turtle.Screen()

   myPoints = [[-100,-50],[0,100],[100,-50]]

   sierpinski(myPoints,3,myTurtle)

   myWin.exitonclick()

main()