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

Published on 12 May 2024 09:40 PM
#Javascript

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

This code implements a fractal tree using the HTML canvas element and JavaScript. Here's a breakdown of the code:

  1. HTML:

    • The HTML code defines a canvas element and includes a JavaScript script.

  2. JavaScript:

    • The JavaScript code first sets up the canvas context and initializes variables related to the tree's appearance.

  3. drawTree Function:

    • This function recursively draws a portion of the fractal tree.
    • It takes six parameters: the starting and ending coordinates of the main branch, and the current depth of the recursion.
    • Based on the starting and ending coordinates, it calculates the coordinates of additional branches and draws the tree shape.
    • The tree is drawn using filled polygons and strokes to create a realistic effect.
    • The depth of the recursion determines the number of times the function calls itself, thus creating the fractal pattern.

  4. HSVtoRGB Function:

    • This function is not defined within the provided code but is assumed to be provided elsewhere or copied from a different source.
    • It converts a color specified in the HSV (Hue, Saturation, Value) format to its RGB (Red, Green, Blue) equivalent, which is used to color the tree.

  5. draw Function:

    • This function clears the canvas and calls the drawTree function to draw the entire tree.

  6. SVG Creation:

    • The code includes a portion that generates an SVG representation of a fractal shape using a different algorithm.
    • It creates a nested structure of polygons to form the shape.
    • The generated SVG is then displayed in the browser window.

In summary, this code uses JavaScript and the canvas element to draw a fractal tree. The drawTree function recursively generates the fractal pattern, and the HSVtoRGB function is used to determine the colors of the tree. Additionally, the code includes a separate section for generating an SVG representation of another fractal shape.

Source code in the javascript programming language

<!DOCTYPE html>
<html lang="en">

<head>
    <meta charset="UTF-8">
    <style>
        canvas {
            position: absolute;
            top: 45%;
            left: 50%;
            width: 640px;
            height: 640px;
            margin: -320px 0 0 -320px;
        }
    </style>
</head>

<body>
    <canvas></canvas>
    <script>
        'use strict';
        var canvas = document.querySelector('canvas');
        canvas.width = 640;
        canvas.height = 640;

        var g = canvas.getContext('2d');

        var depthLimit = 7;
        var hue = 0.15;

        function 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);

            g.beginPath();
            g.moveTo(x1, y1);
            g.lineTo(x2, y2);
            g.lineTo(x3, y3);
            g.lineTo(x4, y4);
            g.closePath();

            g.fillStyle = HSVtoRGB(hue + depth * 0.02, 1, 1);
            g.fill();
            g.strokeStyle = "lightGray";
            g.stroke();

            g.beginPath();
            g.moveTo(x3, y3);
            g.lineTo(x4, y4);
            g.lineTo(x5, y5);
            g.closePath();

            g.fillStyle = HSVtoRGB(hue + depth * 0.035, 1, 1);
            g.fill();
            g.strokeStyle = "lightGray";
            g.stroke();

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

        /* copied from stackoverflow */
        function HSVtoRGB(h, s, v) {
            var r, g, b, i, f, p, q, t;

            i = Math.floor(h * 6);
            f = h * 6 - i;
            p = v * (1 - s);
            q = v * (1 - f * s);
            t = v * (1 - (1 - f) * s);
            switch (i % 6) {
                case 0: r = v, g = t, b = p; break;
                case 1: r = q, g = v, b = p; break;
                case 2: r = p, g = v, b = t; break;
                case 3: r = p, g = q, b = v; break;
                case 4: r = t, g = p, b = v; break;
                case 5: r = v, g = p, b = q; break;
            }
            return "rgb("
                + Math.round(r * 255) + ","
                + Math.round(g * 255) + ","
                + Math.round(b * 255) + ")";
        }

        function draw() {
            g.clearRect(0, 0, canvas.width, canvas.height);
            drawTree(275, 500, 375, 500, 0);
        }
        draw();
    </script>

</body>

</html>


let base = [[{ x: -200, y: 0 }, { x: 200, y: 0 }]];
const doc = [...Array(12)].reduce((doc_a, _, lvl) => {
    const rg = step => `0${(80 + (lvl - 2) * step).toString(16)}`.slice(-2);
    return doc_a + base.splice(0).reduce((ga, [a, b]) => {
        const w = (kx, ky) => (kx * (b.x - a.x) + ky * (b.y - a.y)) / 2;
        const [c, e, d] = [2, 3, 2].map((j, i) => ({ x: a.x + w(i, j), y: a.y + w(-j, i) }));
        base.push([c, e], [e, d]);
        return ga + `<polygon points="${[a, c, e, d, c, d, b].map(p => [p.x, p.y])}"/>\n`;
    }, `<g fill="#${rg(20)}${rg(30)}18">\n`) + '</g>\n';
}, '<svg xmlns="http://www.w3.org/2000/svg" width="1200" stroke="white">\n') + '</svg>';

const { x, y } = base.flat().reduce((a, p) => ({ x: Math.min(a.x, p.x), y: Math.min(a.y, p.y) }));
const svg = doc.replace('<svg ', `<svg viewBox="${[x, y, -x - x, -y]}" `);
document.documentElement.innerHTML = svg, ''; // display svg in the browser window

You may also check:How to resolve the algorithm Barnsley fern step by step in the XPL0 programming language
You may also check:How to resolve the algorithm Statistics/Basic step by step in the Hy programming language
You may also check:How to resolve the algorithm ISBN13 check digit step by step in the XPL0 programming language
You may also check:How to resolve the algorithm Reflection/List methods step by step in the C# programming language
You may also check:How to resolve the algorithm Ackermann function step by step in the LFE programming language