## Symmetry in the Burning Ship to higher powers^{n}+c,where z is a point in the complex plane x+i*y, and re(z)=x, im(z)=y. Notice how the even powers are asymmetric, and the odd powers are symmetric about the diagonal. This symmetry seems to be a result of the way that the function factors out. The terms in the odd powers are more symmetrical. for powers of 4n-1, the point u,v will be the same as v,u. for powers of 4n-3, the point u,v will be the same as -v,u. Burning Ship Home | |

Quadratic (|x|+i*|y|) ^{2}+c |
Cubic (sometimes called the Bird of Prey) (|x|+i*|y|) ^{3}+c |

Quartic (|x|+i*|y|) ^{4}+c |
Quintic (|x|+i*|y|) ^{5}+c |

Sixth Power (|x|+i*|y|) ^{6}+c |
Seventh Power (|x|+i*|y|) ^{7}+c |