CODEWITHSUNDEEP
luaiterationfractalsmandelbrot
David
David

Reputation: 733

How can I fix this issue with my Mandelbrot fractal generator?

I've been working on a project that renders a Mandelbrot fractal. For those of you who know, it is generated by iterating through the following function where c is the point on a complex plane:

function f(c, z) return z^2 + c end

Iterating through that function produces the following fractal (ignore the color):

http://www.embedds.com/wp-content/uploads/2010/01/mandelbrot_set_arduino.png

When you change the function to this, (z raised to the third power)

function f(c, z) return z^3 + c end

the fractal should render like so (again, the color doesn't matter):

http://www.relativitybook.com/CoolStuff/erkfractals_powers/Mandelbrot_Set_power_z4_1800.gif
(source: uoguelph.ca)

However, when I raised z to the power of 3, I got an image extremely similar as to when you raise z to the power of 2. How can I make the fractal render correctly? This is the code where the iterations are done: (the variables real and imaginary simply scale the screen from -2 to 2)

--loop through each pixel, col = column, row = row
local real = (col - zoomCol) * 4 / width
local imaginary = (row - zoomRow) * 4 / width 
local z, c, iter = 0, 0, 0
while math.sqrt(z^2 + c^2) <= 2 and iter < maxIter do
    local zNew = z^2 - c^2 + real
    c = 2*z*c + imaginary
    z = zNew
    iter = iter + 1
end

Upvotes: 2

Views: 833

Answers (1)

David
David

Reputation: 733

So I recently decided to remake a Mandelbrot fractal generator, and it was MUCH more successful than my attempt last time, as my programming skills have increased with practice.

I decided to generalize the mandelbrot function using recursion for anyone who wants it. So, for example, you can do f(z, c) z^2 + c or f(z, c) z^3 + c

Here it is for anyone that may need it:

function raise(r, i, cr, ci, pow)
    if pow == 1 then
        return r + cr, i + ci
    end
    return raise(r*r-i*i, 2*r*i, cr, ci, pow - 1)
end

and it's used like this:

r, i = raise(r, i, CONSTANT_REAL_PART, CONSTANT_IMAG_PART, POWER)

Upvotes: 0

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