Lets list and collate facts and thoughts about related but differant Magic details… Spell Circles(materials and incarnations),Spells and their circles/, Components, Conduits…etc.
I was thinking today about all the different Spell circles hinted at in the book…
- Standard drawn circle using, chalk,wax,blood,metals precious and mundane ink…
2.it was hinted the white cliffs could be a spell circle - Human hands/fingers held in a circle (Newtons calming spell and Siobhans Shadow)… more?
- Lacer hinted that the “Circle” could be held in the minds eye
- Spider silk?
- Multiple people holding hands ? i.e. i was thinking that the old “Ring Around the Rosie” game/dance is acutally a spell circle with a ritual chant… what do you folks think?
… - Jewelry… rings, brackets items made of metal and are more or less a circle
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More thoughts on the spider web
… initally thinking using spider silk as the material to draw the circle but what about using an acutal web as the circle and sacrificing the things in the web … flies,bugs ,crabs, cats…the spider herself… maybe she uses the spider as the output -magicially possessed spider ? could give her a emergency spell circle if she was trapped somewhere without access to her supplies/hands 
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Spell arrays have been used since Myrrdin.
They are always circles, certainly: carved, drawn, or burned into a surface. Although free casters can hold them in their minds, and I’m guessing the gestura also hold the circle in their minds even as they create it with their bodies.
But, the circles can connect to each other with lines. And one circle can be inside or outside another. Aside from the fact that you largely don’t want your body inside one, I imagine them like Dennou Coil’s programs: https://pin.it/7iTAA9bnB
They also use other geometric shapes inside: like pentagrams. In fact, we know that there are four elemental plains plus humanity; seems like, air, radiance, water, earth, because Lacer talks about how he finds the pentagram balanced. These inner aspects of the array are also symbolic and functional connecting components and sources.
Components are used up in many spell arrays; although that seems to somewhat depend on the component, and the use. If, for instance, you were using chicken livers as a component, you might use up all the magic, but still be able to eat the livers later. The spark array Burberry teaches is a will expanding array, and it has components that are not used up. On the other hand, in the first spell we see in the story, the components were obliterated.
Re: #5 above, i imagine the biggest limitation to making a circle from several people holding hands is how it seems to be quite difficult for multiple thaumaterges to cast the same spell together. Plus probably some nervousness about casting through ones body, as it seems to lead to Aberrant-hood. (This does not explain how/why esoteric spells like the shadow and calming spells work just fine without normally turning one into a magical abomination.)
Re: Jewelry, putting a spell circle onto a ring or a solid bracelet seems to put the caster’s hand within the area of the spell effect. For some spells (such as, say, a spell to filter poisons and alcohol out of the blood) this could be very beneficial if properly designed. For something like a shield spell, or a stunning spell, it would have to be built with a modified output, as I assume Oliver’s ring was.
Re: Components, many spells seem to use up the components in the circle. The ones that don’t, off the top of my head, are things like the healing spells that draw on living Radient plants, or spells using a component as an example or template, like Lacer’s dragon scale. Certainly all alchemy destroys the components as part of the brewing process, and I imagine Artificery combines the components into the artifacts (though we haven’t seen any of this on the page).
Re: Gilbratha’s cliffs, i expect we’ll discover that they were part of a spell to murder the Titans. I’m certain Myrddin would have looked into such an event, even though the Titans were apparently all dead before he was born.