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mandelbrot.go
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mandelbrot.go
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// Package mandelbrot provides utilities to compute the Mandelbrot set.
package mandelbrot
import (
"math"
"math/cmplx"
)
// Func represents a function that computes the Mandelbrot set for a given point.
type Func func(complex128) Result
// Result represents a result of the Mandelbrot set computation for a point.
type Result struct {
Bounded bool
Iter int
Abs float64
}
// New returns a new [Func].
func New(maxIter int) Func {
return newPow2(maxIter)
}
// NewPow returns a new [Func] that uses the given power.
func NewPow(maxIter int, pow float64) Func {
if f, ok := newPows[pow]; ok {
return f(maxIter)
}
return newPow(maxIter, pow)
}
var newPows = map[float64]func(maxIter int) Func{
2: newPow2,
3: newPow3,
4: newPow4,
5: newPow5,
6: newPow6,
7: newPow7,
8: newPow8,
9: newPow9,
10: newPow10,
11: newPow11,
12: newPow12,
13: newPow13,
14: newPow14,
15: newPow15,
16: newPow16,
17: newPow17,
18: newPow18,
19: newPow19,
20: newPow20,
}
func newPow2(maxIter int) Func {
return func(c complex128) Result {
// optimization: skip first bulb/cardioid
const quarter = 1.0 / 4.0
foo := real(c) - quarter
imagCSquare := imag(c) * imag(c)
q := foo*foo + imagCSquare
if q*(q+foo) < imagCSquare*quarter {
return Result{
Bounded: true,
Iter: maxIter,
}
}
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z = z*z + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow3(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z3 := z * z2
z = z3 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow4(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z = z4 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow5(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z5 := z * z4
z = z5 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow6(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z6 := z2 * z4
z = z6 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow7(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z6 := z2 * z4
z7 := z * z6
z = z7 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow8(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z = z8 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow9(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z9 := z * z8
z = z9 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow10(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z10 := z2 * z8
z = z10 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow11(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z10 := z2 * z8
z11 := z * z10
z = z11 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow12(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z12 := z4 * z8
z = z12 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow13(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z12 := z4 * z8
z13 := z * z12
z = z13 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow14(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z12 := z4 * z8
z14 := z2 * z12
z = z14 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow15(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z5 := z * z4
z10 := z5 * z5
z15 := z5 * z10
z = z15 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow16(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z16 := z8 * z8
z = z16 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow17(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z16 := z8 * z8
z17 := z * z16
z = z17 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow18(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z16 := z8 * z8
z18 := z2 * z16
z = z18 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow19(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z16 := z8 * z8
z18 := z2 * z16
z19 := z * z18
z = z19 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow20(maxIter int) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z2 := z * z
z4 := z2 * z2
z8 := z4 * z4
z16 := z8 * z8
z20 := z4 * z16
z = z20 + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}
func newPow(maxIter int, pow float64) Func {
return func(c complex128) Result {
z := c
for iter := 0; iter < maxIter; iter++ {
// optimization: calculate "abs square" instead of "abs"
absSquare := real(z)*real(z) + imag(z)*imag(z)
if absSquare > 4 {
return Result{
Bounded: false,
Iter: iter,
Abs: math.Sqrt(absSquare),
}
}
z = cmplx.Pow(z, complex(pow, 0)) + c
}
return Result{
Bounded: true,
Iter: maxIter,
}
}
}