I found this weird red and yellow thing in this shot taken using an EOS Rebel 1200D and the lens that came with it.
It looks surprisingly good; how can I control and replicate these effects?
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So, that's not chromatic aberration, it's lens flare or halo. This is usually caused by shooting with the sun in front of the lens, but not directly in the image, resulting in reflections within the lens system creating that halo effect.
Learning to control that in an artistic manner takes some practice, but done well it can produce a nice effect. In any event, it's really about experimenting with the lens you're using (each will be a different) and leaving off the lens hood. Trial and error, with purpose, will allow you to start to get a feel for it.
The strip of colour near the centre of the image is the result of what is known as lens flare. This occurs due to light directly from a bright source within, or just outside, the field of view being reflected between the lens elements, and so producing a patch of (usually yellow/orange) light that doesn't appear to belong.
To replicate the effect, point your camera near (BUT NEVER AT) the sun and experiment with different angles.