Fractals Interpolation and Extrapolation of Fractals - xbdev.net 2000 - 2024 (c) - Tutorials - Demos - Software, Game Development, Engineering, Data Mining, File Formats,Programming, Machine Learning

<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Fractal Interpolation</title>
    <style>
        canvas {
            border: 1px solid black;
        }
    </style>
</head>
<body>
    <canvas id="canvas" width="600" height="400"></canvas>
    <script>
        const canvas = document.getElementById('canvas');
        const ctx = canvas.getContext('2d');

// Function to generate the Mandelbrot set
        function mandelbrot(x0, y0, maxIter) {
            let x = 0;
            let y = 0;
            let iter = 0;
            while (x * x + y * y <= 4 && iter < maxIter) {
                let xtemp = x * x - y * y + x0;
                y = 2 * x * y + y0;
                x = xtemp;
                iter++;
            }
            return iter / maxIter;
        }

// Function to generate the Julia set
        function julia(x, y, cReal, cImaginary, maxIter) {
            let iter = 0;
            while (x * x + y * y <= 4 && iter < maxIter) {
                let xtemp = x * x - y * y + cReal;
                y = 2 * x * y + cImaginary;
                x = xtemp;
                iter++;
            }
            return iter / maxIter;
        }

// Draw Mandelbrot set
        function drawMandelbrot() {
            const maxIter = 100;
            for (let i = 0; i < canvas.width; i++) {
                for (let j = 0; j < canvas.height; j++) {
                    const x0 = (i - canvas.width / 2) * 4 / canvas.width;
                    const y0 = (j - canvas.height / 2) * 4 / canvas.height;
                    const brightness = mandelbrot(x0, y0, maxIter);
                    const color = Math.floor(255 * brightness);
                    ctx.fillStyle = `rgb(${color},${color},${color})`;
                    ctx.fillRect(i, j, 1, 1);
                }
            }
        }

// Draw Julia set
        function drawJulia(cReal, cImaginary) {
            const maxIter = 100;
            for (let i = 0; i < canvas.width; i++) {
                for (let j = 0; j < canvas.height; j++) {
                    const x = (i - canvas.width / 2) * 4 / canvas.width;
                    const y = (j - canvas.height / 2) * 4 / canvas.height;
                    const brightness = julia(x, y, cReal, cImaginary, maxIter);
                    const color = Math.floor(255 * brightness);
                    ctx.fillStyle = `rgb(${color},${color},${color})`;
                    ctx.fillRect(i, j, 1, 1);
                }
            }
        }

// Interpolate between Mandelbrot and Julia sets
        function interpolateFractals(t) {
            const cReal = -0.8 + t * (0.8);
            const cImaginary = 0.156 + t * (-0.156);
            drawJulia(cReal, cImaginary);
        }

// Main function
        function main() {
            drawMandelbrot();
            // Interpolate between Mandelbrot and Julia sets
            for (let t = 0; t <= 1; t += 0.01) {
                setTimeout(() => {
                    ctx.clearRect(0, 0, canvas.width, canvas.height);
                    interpolateFractals(t);
                }, t * 1000);
            }
        }

main();
    </script>
</body>
</html>

Fractals > Interpolation and Extrapolation of Fractals

Interpolating Between Mandelbrot and Julia set