Zama brought up something today that I think will be a helpful perspective on spirals. Hereby I bring part of our discussion.
zama: Many of our spirals resemble Fermat’s Spirals. I’m curious if there is a way to gauge how close we can get to them?
eli: I think it has to with how you fill the loops out inbetween the sliding stems that are creating the spiral.
If you make an even number of loop bases on both sides, you will get a straight stem. I have a puzzle demonstrating.
Or rather I have 3 puzzles, that may get you a sense of it. https://eternagame.org/web/puzzle/9023368/
https://eternagame.org/web/puzzle/9024748/
https://eternagame.org/web/puzzle/9007424/
zama: @Thanks- and here I’ve been trying to avoid doing player puzzles lately- lol!
eli: In fibonacci spirals the spiral is growing, it isn’t equally close all the way. To create a growing spiral you will need to add more single bases in loops on both sides in a growing pattern.
Hehe
you can usually count on mine having something to do with lab.
Unless cynwulf has got me curious on something. 
zama: The Fermat Spiral doesn’t grow like the Fibonacci- why I thought ours looked more like a Fermat
eli: Ah, yes, I see I misunderstood
https://i.pinimg.com/236x/fe/90/ce/fe90cea2119fc32c69aeb6fcfece298e–alchemy-spirals.jpg
Ok, then you should be perfectly fine with even side loops on both sides of the sliding stems
as this puzzle
https://eternagame.org/web/puzzle/9023368/
Actually the sides in the above image seems to get smaller (edited)
zama: Do you think the Fermat could be duplicated in design?
eli: I think it already has
That Pi design, as I recall it has the fermat patterns as what you showed
zama:
I wondering if the closer a design is to matching the Fermat equation the better the score??
eli: GCACCAGGUACGGAUACCAGACGUUGCCAAACAGGGUGACAUGAGGAUCACCCAUGUACUGUCCCUUGGCAGCCGUACCUGGUGC
That is a fine hypothesis
Now the spiral doesn’t go the whole way through both of them. But there is a black strong line suggesting a bond will form and connect the two spirals. (with light green highlight)
Perhaps easier to see now:
Link to Pi’s design: https://eternagame.org/game/browse/7559902/?filter1_arg1=7612876&filter1=Id&filter1_arg2=761…
zama: The design of yours that I posted above looks closer to me.
eli: Can you give me a link to it?
zama: It’s from the google doc your working on. https://eternagame.org/game/browse/8787266/?filter1=Id&filter1_arg2=9037947&filter1_arg1=903…
eli: Mine only gets one full spiral through
Try play with the chain marker in the arc plot tool. First unmark, then choose chain. You can shift color by holding down shift
What I mean your fermat spiral image has two intertwined spirals both originating from the center of the sequence.
That is almost what Pi’s design does
zama: Ok, it looks more like the Fermat image you posted.
eli: Yup. single fermat
I like this fermat illustration as the color contrast hightlights the inverted mirroring.
found it here: https://codea.io/talk/discussion/1770/fermats-spiral-another-experiment-with-large-images-meshes-and…
I see that the spiral arc plot you posted next to your fermat image is single spiral. But your fermat image is double spiral, just as my fermat image is single spiral. Both kind of arc plots are there. My arc plot represents the single fermat image and Pi’s arc plot represent the two nested fermat spirals. (edited)
So really when we vote for spirals we should vote for 8 different types of designs. 
4 single fermat spiral types + 4 double fermat spiral types
Recipe for double spirals
Ok, I’m not sure the double spirals are possible in same state labs. Pi’s design is an exclusion lab. And there the aptamers have to counter each other. One be on in one state and another be on in another state.
Actually there are. They just look a bit different to Pi’s exclusion double spiral. They instead get a characteristic snail shape.
Here is a good example from a previous post.
It is from Dl2007’s design with fold ratio 1.13 (from Lightning round 4 results).
Watching Dl2007’s design, I think the road to making double spirals is to focus on one of the aptamers. Then to pick two spots in this aptamer that can both pair with themselves in one state (1) and then have these two spots bind two places else in state 2, and have those two new partner spots in state 2 perhaps bind somewhere in state 1.
Kind of like this:
While we haven’t seen high scores for double spiral designs yet, I would like to see them getting made and also voted for just as the same 4 types that I wish to see single spirals for.