  In this study, we develop a numerical method to generate images on an
observer's screen, formed by radiation from hotspots on any timelike orbits
outside a black hole. This method uses the calculation of fractional numbers,
enabling us not only to produce the overall image but also to distinguish
between primary, secondary, and higher-order images. Building upon this, we
compute the images of hotspots from eight potential types of geodesic timelike
orbits outside a Kerr black hole, summarizing the properties of both the
overall and individual order images. Furthermore, we calculate the centroid
motion and lightcurve. Notably, we observe flare phenomena across all orbit
types and classify these flares into three categories based on the Doppler and
gravitational redshift effects.
