Fill under a fractal curve

Question

I am creating a class that I will use for my notes and, as the front page, I intended to have a fractal running through the diagonal of the page and the two parts created by the path, filled with different colors.

As you can see in the image I managed to get the fractal but the fill does not properly work. I have tried different approaches: using \filldraw while creating the fractal, using path picture as shown in this question and answer, clipping and more but none of them gave different results than what you can see in the following picture.

This picture was created by the following code:

\documentclass{article}

\usepackage{tikzpagenodes}
\usetikzlibrary{decorations.fractals}

\begin{document}
\begin{tikzpicture}[overlay, remember picture]
  \fill[blue] (current page.north west) rectangle (current page.south east);
  \filldraw[fill=red,decoration=Koch curve type 2,draw=white,very thick]
    decorate {
      decorate {
        decorate {
          (current page.north west) --
          (current page.south east)
        }
      }
    };
\end{tikzpicture}
\end{document}

I am then trying to understand how I can properly achieve what I want. What options are there? Thanks for your time!

Answer 1

As suggested by Phelype Oleinik in the comments, here's the fixed code:

\documentclass{article}

\usepackage{tikzpagenodes}
\usetikzlibrary{decorations.fractals}

\begin{document}
\begin{tikzpicture}[overlay, remember picture]
  \fill[blue] (current page.north west) rectangle (current page.south east);
  \fill[fill=red,decoration=Koch curve type 2,very thick]
    decorate {
      decorate {
        decorate {
          (current page.north west) --
          (current page.south east)
        }
      }
    } -- (current page.south west) -- cycle;
  \draw[draw=white,decoration=Koch curve type 2,very thick]
    decorate {
      decorate {
        decorate {
          (current page.north west) --
          (current page.south east)
        }
      }
    };
\end{tikzpicture}
\end{document}