Rename variable for number in complex plane from z0 to c

Author: joweich

README.md

@@ -56,14 +56,14 @@ go build
 
 ## About the Algorithm
 ### The Math in a Nutshell
-The Mandelbrot set is defined as the set of complex numbers $z_0$ for which the series 
+The Mandelbrot set is defined as the set of complex numbers $c$ for which the series 
 
-$$z_{n+1} = z²_n + z_0$$
+$$z_{n+1} = z²_n + c$$
 
-is bounded for all $n ≥ 0$. In other words, $z_0$ is part of the Mandelbrot set if $z_n$ does not approach infinity. This is equivalent to the  magnitude $|z_n| ≤ 2$ for all $n ≥ 0$.
+is bounded for all $n ≥ 0$. In other words, $c$ is part of the Mandelbrot set if $z_n$ does not approach infinity. This is equivalent to the  magnitude $|z_n| ≤ 2$ for all $n ≥ 0$.
 
 ### But how is this visualized in a colorful image?
-The image is interpreted as complex plane, i.e. the horizontal axis being the real part and the vertical axis representing the complex part of $z_0$. 
+The image is interpreted as complex plane, i.e. the horizontal axis being the real part and the vertical axis representing the complex part of $c$. 
 
 The colors are determined by the so-called **naïve escape time algorithm**. It's as simple as that: A pixel is painted in a predefined color (often black) if it's in the set and will have another color if it's not. The color is determined by the number of iterations $n$ needed for $z_n$ to exceed $|z_n| = 2$. This $n$ is the escape time, and $|z_n| ≥ 2$ is the escape condition. In our implementation, this is done via the _hue_ parameter in the [HSL color model](https://en.wikipedia.org/wiki/HSL_and_HSV) for non-grayscale images, and the _lightness_ parameter for grayscale images.
 

benchmark_test.go

@@ -112,15 +112,15 @@ func BenchmarkGetColorFromMandelbrotUnlimited(b *testing.B) {
 func BenchmarkRunMandelbrot(b *testing.B) {
 	benchmarkConfig := getBenchmarkConfig()
 
-	z0 := complex(-0.5, 0) // (-0.5, 0) is part of the mandelbrot set, i.e. zn is bounded for all zn
+	c := complex(-0.5, 0) // (-0.5, 0) is part of the mandelbrot set, i.e. zn is bounded for all zn
 	for _, maxIter := range benchmarkConfig.MaxIterValues {
 		testId := fmt.Sprintf("MaxIter_%d", maxIter)
 		b.Run(testId, func(subB *testing.B) {
 			imgConf.MaxIter = maxIter
 			subB.ResetTimer()
 
 			for i := 0; i < subB.N; i++ {
-				runMandelbrot(z0)
+				runMandelbrot(c)
 			}
 		})
 	}

mandelbrot.go

@@ -6,8 +6,8 @@ import (
 	"math/cmplx"
 )
 
-func getColorForComplexNr(z0 complex128) color.RGBA {
-	return getColorFromMandelbrot(runMandelbrot(z0))
+func getColorForComplexNr(c complex128) color.RGBA {
+	return getColorFromMandelbrot(runMandelbrot(c))
 }
 
 func getColorFromMandelbrot(isUnlimited bool, magnitude float64, iterations int) color.RGBA {
@@ -27,15 +27,15 @@ func getColorFromMandelbrot(isUnlimited bool, magnitude float64, iterations int)
 	}
 }
 
-func runMandelbrot(z0 complex128) (bool, float64, int) {
+func runMandelbrot(c complex128) (bool, float64, int) {
 	var z complex128
 
 	for i := 0; i < imgConf.MaxIter; i++ {
 		magnitude := cmplx.Abs(z)
 		if magnitude > 2 {
 			return true, magnitude, i
 		}
-		z = z*z + z0
+		z = z*z + c
 	}
 	return false, 0, 0
 }