  The mathematical treatment and graphical representation of Special Relativity
(SR) are well established, yet carry deep implications that remain hard to
visualize. This paper presents a new graphical interpretation of the geometry
of SR that may, by complementing the standard works, aid the understanding of
SR and its fundamental principles in a more intuitive way. From the axiom that
the velocity of light remains constant to any inertial observer, the geodesic
is presented as a line of constant angle on the complex plane across a set of
diverging reference frames. The resultant curve is a logarithmic spiral, and
this view of the geodesic is extended to illustrate the relativistic Doppler
effect, time dilation, length contraction, the twin paradox, and relativistic
radar distance in an original way, whilst retaining the essential mathematical
relationships of SR. Using a computer-generated graphical representation of
photon trajectories allows a visual comparison between the relativistic
relationships and their classical counterparts, to visualize the consequences
of SR as velocities become relativistic. The model may readily be extended to
other situations, and may be found useful in presenting a fresh understanding
of SR through geometric visualization.
