Getting a computer to generate i

[Loli]

As we all know, there is the imaginary plane.
So I have i (root -1)
How would I go about calculating this on a computer? I know that it is impossible, it cannot be done, but I am trying to make a Mandelbrot and I was just wandering how you would go about doing this.

[esalaka]

[url=http://www.cplusplus.com/reference/std/complex/]Hello C++ standard library.[/url]

[editline]22nd October 2010[/editline]

That aside, I recall there's at least one way of writing a Mandelbrot fractal without imaginary numbers.

[Loli]

Hmm. That C++ isn't useful as I don't know C++ well enough to do this. But could you provide a link for Mandelbrot without imaginary numbers?

[esalaka]

Use the imaginary part as the y component and the real part as the x component?

[Loli]

Could work, I'd have to take a look at it. Bit busy at the moment though :P

[esalaka]

Actually, the Mandelbrot fractal seems to be a plotting of the Mandelbrot set on the complex plane, where x is the real part and y is the imaginary part.

So it would work, you'd just have to scale the values, obviously, to get a reasonably sized one (The values of the set are apparently in the range (-2…1, -1…1) )

The scaling is done like this, if someone's interested:
[cpp]
screenX = minScreenX + ( ( origX + 2 ) / ( 1 + 2 ) ) * ( maxScreenX - minScreenX ) // For x
screenY = minScreenY + ( ( origY + 1 ) / ( 1 + 1 ) ) * ( maxScreenY - minScreenY ) // For y
[/cpp]

[larikang]

[QUOTE=Loli;25568152] I know that it is impossible, it cannot be done, but I am trying to make a Mandelbrot and I was just wandering how you would go about doing this.[/QUOTE]
That's just plain wrong.

Almost any mathematical system can be programmed on a computer. Math follows extremely strict rules and programming languages excel at expressing systems that follow strict, well-defined rule sets. Just because most languages use real numbers for their usual arithmetic doesn't mean it's impossible to program with imaginary numbers. I recall another thread where multiple said that it's similarly "impossible" to make a graphics library that would use spherical - rather than Euclidean - geometry. Ridiculous.

Quick'n'dirty complex numbers in Ruby:

class ComplexNumber
	attr_accessor :real, :imaginary
	
	def initialize(real, imaginary)
		@real = real
		@imaginary = imaginary
	end
	
	def +(n)
		return ComplexNumber.new(@real + n.real, @imaginary + n.imaginary)
	end
	
	def *(n)
		return ComplexNumber.new(@real * n.real - @imaginary * n.imaginary, @real * n.imaginary + n.real * @imaginary)
	end
	
	def to_s
		return "#{@real} + #{@imaginary}i"
	end
end

Actually Ruby is an ideal language for working with complex numbers, because you can override standard library functions. So I could even do something like

class Numeric
	def **(x) #exponentiation
		if self < 0
			return ComplexNumber.new(0, (-1 * self) ** x)
		else
			...
		end
	end
end

so then (-1)**(0.5) would even return i as expected.

[Siemens]

[QUOTE=Larikang;25580361]Actually Ruby is an ideal language for working with complex numbers, because you can override standard library functions.[/QUOTE]

Operator overloading is a pretty common feature in OOP languages.

[jA_cOp]

[QUOTE=Siemens;25580470]Operator overloading is a pretty common feature in OOP languages.[/QUOTE]

That's not what he meant. He uses operator overloading in the first code snippet too. The second snippet demonstrates Ruby's open classes: Numeric is the base class for all Ruby number classes.

[Siemens]

[QUOTE=jA_cOp;25580864]The second snippet demonstrates Ruby's open classes: Numeric is the base class for all Ruby number classes.[/QUOTE]

Oh, didn't see that. That's awesome!