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

Published on 12 May 2024 09:40 PM
#Processing

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

Source code in the processing programming language

void tree(float x1, float y1, float x2, float y2, int depth) {

  if (depth <= 0) {
    return;
  }

  float dx = (x2 - x1);
  float dy = (y1 - y2);

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

  // square
  beginShape();
  fill(0.0, 255.0/depth, 0.0);
  vertex(x1, y1);
  vertex(x2, y2);
  vertex(x3, y3);
  vertex(x4, y4);
  vertex(x1, y1);
  endShape();

  // triangle
  beginShape();
  fill(0.0, 255.0/depth, 0.0);
  vertex(x3, y3);
  vertex(x4, y4);
  vertex(x5, y5);
  vertex(x3, y3);
  endShape();

  tree(x4, y4, x5, y5, depth-1);
  tree(x5, y5, x3, y3, depth-1);
}  

void setup() {
  size(1920, 1080);
  background(255);
  stroke(0, 255, 0);
  tree(width/2.3, height, width/1.8, height, 10);
}


def setup():
    size(800, 400)
    background(255)
    stroke(0, 255, 0)
    tree(width / 2.3, height, width / 1.8, height, 10)


def tree(x1, y1, x2, y2, depth):
    if depth <= 0: return
    dx = (x2 - x1)
    dy = (y1 - y2)

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

    # square
    beginShape()
    fill(0.0, 255.0 / depth, 0.0)
    vertex(x1, y1)
    vertex(x2, y2)
    vertex(x3, y3)
    vertex(x4, y4)
    vertex(x1, y1)
    endShape()

    # triangle
    beginShape()
    fill(0.0, 255.0 / depth, 0.0)
    vertex(x3, y3)
    vertex(x4, y4)
    vertex(x5, y5)
    vertex(x3, y3)
    endShape()

    tree(x4, y4, x5, y5, depth - 1)
    tree(x5, y5, x3, y3, depth - 1)

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