Rigorous bounds for polynomial Julia sets

We present an algorithm for computing images of polynomial Julia setsthat are reliable in the sensethat they carry mathematical guarantees againstsampling artifacts and rounding errors in floating-point arithmetic.We combine cell mappingbased on interval arithmeticwith label propagation in graphsto avoid function iteration and rounding errors.As a result,our algorithm avoids point sampling and canreliably classify entire rectanglesin the complex plane as being on either side of the Julia set.The union of the rectangles that cannot be so classified is guaranteedto contain the Julia set.Our algorithm computes a refinable quadtree decomposition of the complex planeadapted to the Julia set which can be used for rendering and forapproximating geometric propertiessuch asthe area of the filled Julia set andthe fractal dimension of the Julia set.