Fractals/Snowflake.m at master · PrParadoxy/Fractals · GitHub

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function v = Snowflake(n, resolution)

% Koch Snowflake inspired by
% https://codereview.stackexchange.com/questions/144700/plotting-the-koch-snowflake

% n: Iteration number
% resolution: number of grid points per dimension

L = 1;
p1 = [0, 0];
p2 = [1/2, L*sin(pi/3)] ;
p3 = [L, 0];
centroid = (p1 + p2 + p3)/3;

flake_points = [p1 - centroid; p2 - centroid; p3 - centroid];

x = linspace(-1, 1, resolution);
y = linspace(-1, 1, resolution);
v = Triangle(1, x, y, flake_points);

for j = 1:n

    n_points = size(flake_points,1);
    new_triangle_points = nan(n_points*3,2);
    for i = 1:n_points
        p = flake_points(i,:);

        if i == n_points
            vector = flake_points(1,:)-flake_points(i,:);
        else
            vector = flake_points(i+1,:)-flake_points(i,:);
        end

        b1 = p + 1/3*vector;
        b2 = p + 1/2*vector + perp(vector)*L/3*sin(pi/3);
        b3 = p + 2/3*vector;
        new_triangle_points(3*i-2:3*i,:) = [b1; b2; b3];
        v = v + Triangle(1, x, y, [b1; b2; b3]);
    end


    flake_points(end+1:end+9,:) = nan(9,2);
    new_flake_points = nan(n_points*3+n_points,2);
    n = 1;
    for i = 1:n_points
        new_flake_points(n,:) = flake_points(i,:);
        index = 3*i-2;
        new_flake_points(n+1:n+3,:) = new_triangle_points(index:index+2,:);
        n = n + 4;
    end
    flake_points = new_flake_points;
    L = 1/3*L;

end

    function p_vec = perp(vec)

        p_vec(1) = -vec(2);
        p_vec(2) = vec(1);
        p_vec = p_vec / norm(p_vec);

    end
end