This is amazing! Can you do the reverse, illuminating strips of the Buddhabrot and highlighting which parts of this strip just outside the Mandebrot visit it?
Thank you! I don't think so, the problem is quite hard, it's not as simple as solving an equation. In other words, in the Mandelbrot set you get the pixel and then do the maths, with Buddhabrot you first do the maths and then you get the pixel as result. With the huge enough amount of memory and a lot of time you could do something like what you say.
@@TomRathborne can you mount the napkin in a RAM slot? I will think about the idea. Probably if the values are discretized the space requirements may be lowered.
Technically yes, but it's very hard. The idea would be: Consider both z and c complex numbers. First pre-compute the orbits (values of z) for each value of c that is selected. How to select proper values for c is a challenge for itself. So you have lots of values of c (produces pixels on the mandelbrot set) and for each of them a lot of values of z (produces pixels on the buddhabrot). When I say a lot it's on the order of thousands or millions. So the relation is like one c to many z and it has to be changed in a way that gives one z to many c. This can be done by some kind rounding. Once you have a table that goes from z to many c you just choose some order for the values of z and render it on the picture.
This is amazing! Can you do the reverse, illuminating strips of the Buddhabrot and highlighting which parts of this strip just outside the Mandebrot visit it?
Thank you! I don't think so, the problem is quite hard, it's not as simple as solving an equation.
In other words, in the Mandelbrot set you get the pixel and then do the maths, with Buddhabrot you first do the maths and then you get the pixel as result.
With the huge enough amount of memory and a lot of time you could do something like what you say.
@@FalkBay indeed, at the bottom of the back of my napkin it says 64TB.
@@TomRathborne can you mount the napkin in a RAM slot? I will think about the idea. Probably if the values are discretized the space requirements may be lowered.
Technically yes, but it's very hard. The idea would be:
Consider both z and c complex numbers.
First pre-compute the orbits (values of z) for each value of c that is selected. How to select proper values for c is a challenge for itself.
So you have lots of values of c (produces pixels on the mandelbrot set) and for each of them a lot of values of z (produces pixels on the buddhabrot). When I say a lot it's on the order of thousands or millions.
So the relation is like one c to many z and it has to be changed in a way that gives one z to many c. This can be done by some kind rounding.
Once you have a table that goes from z to many c you just choose some order for the values of z and render it on the picture.
@@FalkBay like I said elsewhere, sparse matrix storage might work. Unfortunately my napkin is not a cabinet full of futuristic phase-change storage.
Looks like soem kind of xray scan
Ok, if you mind