A positive answer to a symmetry conjecture on homogeneous IFS

This paper positively answers 'Open Question 1' posed by Feng and Wang in 2009. The theorem states that if two homogeneous Iterated Function Systems (IFS) satisfy the Open Set Condition (OSC), share the same attractor K, and their common contraction factors are opposite to each other, then the attractor K is symmetric. This result has implications for understanding the geometry of fractals and their construction, with potential applications in image compression, computer graphics, and modeling natural patterns.