This was a simple approach to draw fractal structures with Javascript and the 2D context.
Turned out that this is possible but not very quick. Better use WebGL/GLSL and hardware acceleration for tasks like this.
There a WebGL implementation for this at https://www.int2byte.de/public/webgl_playground/05_fractal_test/main.html
The source for that is here https://github.com/IkarosKappler/webgl_playground/tree/master/05_fractal_test