How to resolve the algorithm Pythagoras tree step by step in the Wren programming language

Published on 12 May 2024 09:40 PM
#Wren

How to resolve the algorithm Pythagoras tree step by step in the Wren programming language

Table of Contents

Problem Statement

The Pythagoras tree is a fractal tree constructed from squares. It is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to represent the Pythagorean theorem.

Construct a Pythagoras tree of order 7 using only vectors (no rotation or trigonometric functions).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pythagoras tree step by step in the Wren programming language

Source code in the wren programming language

import "graphics" for Canvas, Color
import "dome" for Window
import "./polygon" for Polygon

var DepthLimit = 7
var Hue = 0.15

class PythagorasTree {
    construct new(width, height) {
        Window.title = "Pythagoras Tree"
        Window.resize(width, height)
        Canvas.resize(width, height)
    }

    init() {
        Canvas.cls(Color.white)
        drawTree(275, 500, 375, 500, 0)
    }

    drawTree(x1, y1, x2, y2, depth) {
        if (depth == DepthLimit) return
        var dx = x2 - x1
        var dy = y1 - y2

        var x3 = x2 - dy
        var y3 = y2 - dx
        var x4 = x1 - dy
        var y4 = y1 - dx
        var x5 = x4 + 0.5 * (dx - dy)
        var y5 = y4 - 0.5 * (dx + dy)

        // draw a square
        var col = Color.hsv((Hue + depth * 0.02) * 360, 1, 1)
        var square = Polygon.quick([[x1, y1], [x2, y2], [x3, y3], [x4, y4]])
        square.drawfill(col)
        square.draw(Color.lightgray)

        // draw a triangle
        col = Color.hsv((Hue + depth * 0.035) * 360, 1, 1)
        var triangle = Polygon.quick([[x3, y3], [x4, y4], [x5, y5]])
        triangle.drawfill(col)
        triangle.draw(Color.lightgray)

        drawTree(x4, y4, x5, y5, depth + 1)
        drawTree(x5, y5, x3, y3, depth + 1)
    }

    update() {}

    draw(alpha) {}
}

var Game = PythagorasTree.new(640, 640)

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