mandelbrot3

Exercise 3.8

"Rendering fractals at high zoom levels demands great arithmetic precision. Implement the same fractal using four different representations of numbers: complex64, complex128, big.Float, and big.Rat. [...] How do they compare in performance and memory usage? At what zoom levels do rendering artifacts become visible?"

Benchmarks

I have omitted the results for big.Rat because it is horrendously slow.

$ go test ./mandelbrot -bench=. -benchmem
goos: windows
goarch: amd64
pkg: github.com/masonelmore/gopl/ch3/ex3.8/mandelbrot
BenchmarkRenderFuncs/complex64-256-12                100          20691184 ns/op          761342 B/op     124781 allocs/op
BenchmarkRenderFuncs/complex64-512-12                 20          82304710 ns/op         3045562 B/op     499191 allocs/op
BenchmarkRenderFuncs/complex64-1024-12                 5         328818800 ns/op        12182304 B/op    1996979 allocs/op
BenchmarkRenderFuncs/complex64-2048-12                 1        1313075100 ns/op        48730240 B/op    7988227 allocs/op
BenchmarkRenderFuncs/complex128-256-12               100          18171040 ns/op          761342 B/op     124785 allocs/op
BenchmarkRenderFuncs/complex128-512-12                20          71954115 ns/op         3045432 B/op     499197 allocs/op
BenchmarkRenderFuncs/complex128-1024-12                5         289616560 ns/op        12182390 B/op    1996997 allocs/op
BenchmarkRenderFuncs/complex128-2048-12                1        1153066000 ns/op        48730400 B/op    7988263 allocs/op
BenchmarkRenderFuncs/bigfloat-256-12                   1        1244071200 ns/op        448436624 B/op   9451068 allocs/op
BenchmarkRenderFuncs/bigfloat-512-12                   1        4963283900 ns/op        1798066912 B/op 37895046 allocs/op
BenchmarkRenderFuncs/bigfloat-1024-12                  1        19748129500 ns/op       7204265376 B/op 151831295 allocs/op
BenchmarkRenderFuncs/bigfloat-2048-12                  1        79995575500 ns/op       28837111728 B/op        607745380 allocs/op
PASS
ok      github.com/masonelmore/gopl/ch3/ex3.8/mandelbrot        121.219s

Artifacts

Interestingly big.Float appears to show artifacts around the same zoom level of complex128. This is probably because all of the Render funcs use float64 to set the bounds of the image. I have not yet tested if this is the case.

complex64

Artifacts appear around a zoom level of 1e-05.

complex128

Artifacts appear around a zoom level of 1e-14.

big.Float

Artifacts appear around a zoom level of 1e-14.