This is cool
https://www.desmos.com/calculator/hsowmvsyua
This shows 200 iterations of the complex number 'c' by using the Mandelbrot set formula. The next iteration makes a new point and it connects to the previous one with a line. The next iteration is always the previous one squared plus 'c'. So it looks like this:
1. iteration = c
2. iteration = c^2 + c
3. iteration = (c^2 + c)^2 + c
4. iteration = ((c^2 + c)^2 + c)^2 + c
etc...
The Mandelbrot set is basically the region of all complex numbers with the condition that iterating it will never produce an absolute value greater than 2. The number 2 is important because if the absolute value was more than that, adding more iterations would make it grow towards infinity. The shaded region is the region where you can put the point C so that the graph stays inside the red circle. It makes nice patterns if you click and drag it and try to put it close the to edge.
Complex numbers don't work on Desmos so I used points to simulate complex numbers. There would have been probably some more efficient way to do it but at least it still works at 2 fps
https://www.desmos.com/calculator/hsowmvsyua
This shows 200 iterations of the complex number 'c' by using the Mandelbrot set formula. The next iteration makes a new point and it connects to the previous one with a line. The next iteration is always the previous one squared plus 'c'. So it looks like this:
1. iteration = c
2. iteration = c^2 + c
3. iteration = (c^2 + c)^2 + c
4. iteration = ((c^2 + c)^2 + c)^2 + c
etc...
The Mandelbrot set is basically the region of all complex numbers with the condition that iterating it will never produce an absolute value greater than 2. The number 2 is important because if the absolute value was more than that, adding more iterations would make it grow towards infinity. The shaded region is the region where you can put the point C so that the graph stays inside the red circle. It makes nice patterns if you click and drag it and try to put it close the to edge.
Complex numbers don't work on Desmos so I used points to simulate complex numbers. There would have been probably some more efficient way to do it but at least it still works at 2 fps
