Hey, Gottfried!
That's not the speed up!!!!!!!!!!!!
The speed up, is if you need to graph 1000x1000 pixels. We only need to reference func(z), b*1000xb*1000 times for \(0 < b \le 1\). Rather than evaluating pixel by pixel. We only evaluate the function func(z) pixel block by pixel block!
So essentially.
If I take: func(z) = sin(z). And I want to make a 1000x1000 pixel graph. I have to evaluate func(z) 1000x1000 times; at each pixel.
Where, if we use my speed up. Set b = 0.5. Then I only need to evaluate func(z) 500x500 times. And still make a 1000x1000 pixel picture. Where I "spline" together the missing pixels.
There's no real speed up for func(z) = sin(z). Because sin(z) graphs so fast. But when we are taking a very complex tetration function it's time consuming to evaluate func!!!
Say that func(z) takes 1 second to evaluate. Then to run mike3's program, we need at least 1000x1000 seconds to graph. Where my speed up is 500x500 seconds.
Think of it as a lossy compression algorithm!!!!!
That's not the speed up!!!!!!!!!!!!
The speed up, is if you need to graph 1000x1000 pixels. We only need to reference func(z), b*1000xb*1000 times for \(0 < b \le 1\). Rather than evaluating pixel by pixel. We only evaluate the function func(z) pixel block by pixel block!
So essentially.
If I take: func(z) = sin(z). And I want to make a 1000x1000 pixel graph. I have to evaluate func(z) 1000x1000 times; at each pixel.
Where, if we use my speed up. Set b = 0.5. Then I only need to evaluate func(z) 500x500 times. And still make a 1000x1000 pixel picture. Where I "spline" together the missing pixels.
There's no real speed up for func(z) = sin(z). Because sin(z) graphs so fast. But when we are taking a very complex tetration function it's time consuming to evaluate func!!!
Say that func(z) takes 1 second to evaluate. Then to run mike3's program, we need at least 1000x1000 seconds to graph. Where my speed up is 500x500 seconds.
Think of it as a lossy compression algorithm!!!!!