...at each petal you can transition into a cateye and between two petals you can transition into a cateye.
At each petal (loop) the poi is in a similar state as it is in the tip of a cateye.
Therefor you have a seamless transition point between the 2.
You can lockout from your flower into a cateye that is pointing radially from the center of your original flower.
On the other hand, in between petals you have an arc that connects 2 loops.
This state is similar to that of the elongated part of a cateye.
Therefor you can make a seamless transition, locking out in a cateye that is perpendicular to the center of your original flower.
So yeah, wherever there is a loop you can lockout into a cateye, and wherever there is an arc you can lock out in a cateye.
But for that matter, wherever there is a loop you can lockout in an isolation, and wherever there is an arc you can lockout in an extension.
From flowers (inspin or antispin), and for that matter any patterns that contain loops and/or arcs in general, you can use 1 of 3 types of unit circle lockouts:
- extension
- isolation
- cateye
Extension has the 2 ends of the poi in a together time - same direction relationship.
This is related to translational symmetry (in this case along the radius in a concentric manner).
Isolation is a split time - same direction relationship of the 2 ends.
This is related to radial symmetry.
Cateyes have the 2 ends relating in opposite directions, in any possible phase, ie, together, split, quarter, and anything in-between for that matter.
This is related to mirror symmetry. The phase dictates the angle of the mirror axis.
These lockouts raise an important point: We should be conscious of the the distinction between closed figures and open figures.
With a closed figure, if you start at time
T1 at position
A you will end at time
T2 at position
A, with a similar poi/momentum state. This means you can repeat the same pattern, in it's entirety,
n times (however many you want).
With an open figure if you start at time
T1 at position
A you will end at time
T2 at position
B, with a poi/momentum state that may or may not be dissimilar.
You can take a closed figure and chop it up into a series of open figures.
For example a circle is a simple closed figure. You could cut it into 4 quarter circles.
However you don't have to put these quarters back together to only make a circle.
You could use some of them combined with other open figures, to assemble another pattern.
This assembly might be a new open figure, or it might be a new closed figure.
It might even be a more complex closed figure that returns to the same poi position/momentum state as the start of your original pattern (ie your circle).
This allows you to transition cyclically between these 2 patterns in a more complex assembly pattern.
One of the ways you can use these transition principles is using some form of lockout, as stated above. If you lockout from the complex pattern for too many cycles, the cohesiveness of your assembly may be lost.
But if you for example, lockout at each petal of a triquetra with one cycle of cateye, you make a pattern that approximates one of the above mentioned 3-order curves.
Notice that I said
approximates!
Is there a difference between lockout assemblies and complex curves with perfect harmonic ratios?Well, yes and no. What the heck do I mean by this anyway?
Let's take a simple example: 2-lockout inspin flower VS 2-loop inspin flower.
Many people learn inspin flowers using lockouts.
For a 2-petal flower they make a longarm half-circle, then lockout into a static circle.
During that time their hand is static.
Then the small circle completes, and their hand makes another longarm half-circle, followed by another static circle...
Finally they have completed 1 cycle of 2-petal flower, and they could continue to do so if they like.
This uses 2 open figures (the 2 half-circles) and 2 closed figures (the 2 static circles).
This presents an interesting problem:
At the 2 points where the poi position/momentum state are the same in the different figures, we could choose to omit a lockout, or lockout for n number of spins, not just one. So this pattern is actually an assembly of simpler harmonic ratios, or parts of them.
Now lets look at a 2-petal inspin that uses 2 loops. It is an accurate recreation of the mathematical curve that has a 2:1 ratio between the 2 Centers of Rotation. You will only come back to a similar position/momentum point once per repetition of the pattern. If you deviate from it, you are then using part or it to create an assembly.
Zaltymbunk is looking at the figures that are irreducible closed figures in themselves. These figures arise out of relatively simple harmonic ratios. From these figures as a base, we can chop them up and make assemblies.
So yes there is an important difference between assembling lockouts, and irreducible harmonic curves... but we as humans will never quite recreate them perfectly.
Further more there are plenty of assemblies that approximate the perfect curves nicely enough for an audience... for that matter, making cool assemblies is a lot of fun.
So no, it isn't all that important to use only perfect harmonic curves, and think in those terms. It is however useful to understand the differences and the relationships between the 2.
Final point:
Wether you think of a 3rd-order curve, or an assembly of cateye lockouts connected by the open figures you chopped out of a triquetra, you will be getting a similar pattern. Understanding the implications of each thought model will give you a variety of creative ways to explore poi.
and 
AKA 1 -4 ; 3/4 1/4 and 1 -2 ; 1/2 1/2 (they are in cycloid case because it is the closest to the polygonal representation).
Previous Topic
Index