In this talk, we will explore the dynamics of a family of logistic maps that connects the main cardioid of the Mandelbrot set \(M\) and \(M\cap\mathbb{R}\). This connection is induced by the magic map \(T(\theta):=\frac{1}{2}+\frac{\theta}{4}\) defined on the set of external argument of the main hyperbolic component \(W_{0}\) of \(M\). For \(c\in\partial W_{0}\) with an irrational internal argument \(\gamma\) and external argument \(\theta\), the external ray \(R(T(\theta))\) will land at a real parameter \(c'\in M\). There are several good properties of this real parameter, for example the quadratic polynomial \(P_{c'}\) does not satisfy the Collet-Eckman condition, and the dynamics of \(P_{c'}\) is semi-conjugate to the a rigid rotation of angle \(\gamma\). To fully understand this family, we will firstly study the case when \(\gamma\) is the Golden mean. To understand this Goldean mean rotation, we analyze the Fibonnaci polynomial corresponding to the Hubbard tree induced by each Fibonnaci quotient. In particular, the kneading invariants and kneading maps of such polynomials play a vital role in this research. The talk will firstly introduce the general setup, motivation, then display several proved properties of Fibonnaci polynomials, and how they connect to the logistic family.