Unfortunately, not really... There are some free or cheap/simple ones, but maybe not so easy to use for planar geometry specifically. Or accurate ones, but you're going to pay for it, and it's not going to be easy to use... Hopefully others more experienced will chime in with suggestions?
Mainly my comment comes from a general familarity of ultra/wideband antennas -- they have a self-similar (scale independent) geometry, so that fields behave the same over a wide range of frequencies. The bowtie is the most likely candidate here. There's a lot of press about general fractal types but it doesn't look like e.g. Koch curves have all that much going for them, honestly; it's the scale-independent ones (typically having some combination of zooming/radial symmetry -- like a cone, hence the conical dipole for example, a bowtie being the planar equivalent). To cover an octave, you don't need to be quite so in-depth (you can get a little space savings still), but it will have to be something more than a plain old wire dipole, and can't be electrically short (LC tuned, or curled/folded up to make a shorter overall shape for a given target frequency -- such an antenna will have a higher Q and thus narrower bandwidth as it only couples with the resonant band, plus whatever harmonics show up, corresponding to the segments it's built from -- the zigzag will likely have some peaks and/or notches at frequencies corresponding to the zig length or zag spacing, though these will be at some octaves above the intended passband I think so not really relevant in this case).
Tim