sheridan_vbulletin3_import9660
New Member
For a while now I've been interested in fractals, the math behind them and the visuals they can produce.I just can't really figure out how to map the mathematical formula to a piece of code that draws the picture.
Given this formula for the mandelbrot set: \[code\]Pc(z) = z * z + c\[/code\]
How does that compare to the following code:\[code\]$outer_adder = ($MaxIm - $MinIm) / $Lines;$inner_adder = ($MaxRe - $MinRe) / $Cols;for($Im = $MinIm; $Im <= $MaxIm; $Im += $outer_adder){ $x=0; for($Re = $MinRe; $Re <= $MaxRe; $Re += $inner_adder) { $zr = $Re; $zi = $Im; for($n = 0; $n < $MaxIter; ++$n) { $a = $zr * $zr; $b = $zi * $zi; if($a + $b > 2) break; $zi = 2 * $zr * $zi + $Im; $zr = $a - $b + $Re; } $n = ($n >= $MaxIter ? $MaxIter - 1 : $n); ImageFilledRectangle($img, $x, $y, $x, $y, $c[$n]); ++$x; } ++$y;}\[/code\]Code is not complete, just showing the main iteration part for brevity.So the question is: could someone explain to me how the math compares to the code?Edit: To be clear, I've found dozens of resources explaining the math, and dozens of resources showing code, but nowhere can I find a good explanation of the two combined.
Given this formula for the mandelbrot set: \[code\]Pc(z) = z * z + c\[/code\]
How does that compare to the following code:\[code\]$outer_adder = ($MaxIm - $MinIm) / $Lines;$inner_adder = ($MaxRe - $MinRe) / $Cols;for($Im = $MinIm; $Im <= $MaxIm; $Im += $outer_adder){ $x=0; for($Re = $MinRe; $Re <= $MaxRe; $Re += $inner_adder) { $zr = $Re; $zi = $Im; for($n = 0; $n < $MaxIter; ++$n) { $a = $zr * $zr; $b = $zi * $zi; if($a + $b > 2) break; $zi = 2 * $zr * $zi + $Im; $zr = $a - $b + $Re; } $n = ($n >= $MaxIter ? $MaxIter - 1 : $n); ImageFilledRectangle($img, $x, $y, $x, $y, $c[$n]); ++$x; } ++$y;}\[/code\]Code is not complete, just showing the main iteration part for brevity.So the question is: could someone explain to me how the math compares to the code?Edit: To be clear, I've found dozens of resources explaining the math, and dozens of resources showing code, but nowhere can I find a good explanation of the two combined.