A side-by-side comparison of the normal cascade, MillsMess, and the reverse cascade. The animations are synchronised so you can see that the timing is identical.  Dwell ratio has been set to 50% so one hand throws exactly as the other hand catches. Throw/catch pairs are in frames 00, 08 and 16.

I hope this shows that MillsMess is just the standard cascade done with the throws and catches in different places, as indeed is the reverse cascade.

We start with a trace of the patterns. This shows the shape made by each pattern, and the relative placements of the balls along the path. You can see that in each case the path is a figure of eight, but in the MillsMess pattern the balls are closer together.

http://www.solipsys.co.uk/new/images/MillsAnalysis/Trace.gif Trace

Here's an animation of each pattern.

http://www.solipsys.co.uk/new/images/MillsAnalysis/Anim.gif Animation

And now frame by frame.

In frame 00 the red is exactly now being caught, the green is exactly now being thrown. The balls are exactly level with each other

http://www.solipsys.co.uk/new/images/MillsAnalysis/00.gif 00

In frame 01 the green ball has only just left the hand, but it is no longer being held. The hand shows a slight follow-through, maintaining close proximity. It has, however, been thrown.

http://www.solipsys.co.uk/new/images/MillsAnalysis/01.gif 01

In frame 02 the separation is now clear.

http://www.solipsys.co.uk/new/images/MillsAnalysis/02.gif 02
http://www.solipsys.co.uk/new/images/MillsAnalysis/03.gif 03

Frame four is exactly halfway between throws and catches.

http://www.solipsys.co.uk/new/images/MillsAnalysis/04.gif 04
http://www.solipsys.co.uk/new/images/MillsAnalysis/05.gif 05
http://www.solipsys.co.uk/new/images/MillsAnalysis/06.gif 06

Frame 07 - the blue is close to the hand but not yet caught.

http://www.solipsys.co.uk/new/images/MillsAnalysis/07.gif 07

Frame 08 shows the instant of the blue catch, and the instant of the red throw. Note that the red throw is exactly centered in the cascade, and the blue catch is exactly centered in the mess and reverse cascade.

http://www.solipsys.co.uk/new/images/MillsAnalysis/08.gif 08

Frame 09 - the red ball has left the hand although the separation is not yet significant.

http://www.solipsys.co.uk/new/images/MillsAnalysis/09.gif 09

''etc.''

http://www.solipsys.co.uk/new/images/MillsAnalysis/10.gif 10
http://www.solipsys.co.uk/new/images/MillsAnalysis/11.gif 11
http://www.solipsys.co.uk/new/images/MillsAnalysis/12.gif 12
http://www.solipsys.co.uk/new/images/MillsAnalysis/13.gif 13
http://www.solipsys.co.uk/new/images/MillsAnalysis/14.gif 14
http://www.solipsys.co.uk/new/images/MillsAnalysis/15.gif 15
http://www.solipsys.co.uk/new/images/MillsAnalysis/16.gif 16
http://www.solipsys.co.uk/new/images/MillsAnalysis/17.gif 17
http://www.solipsys.co.uk/new/images/MillsAnalysis/18.gif 18
http://www.solipsys.co.uk/new/images/MillsAnalysis/19.gif 19
http://www.solipsys.co.uk/new/images/MillsAnalysis/20.gif 20
http://www.solipsys.co.uk/new/images/MillsAnalysis/21.gif 21
http://www.solipsys.co.uk/new/images/MillsAnalysis/22.gif 22
http://www.solipsys.co.uk/new/images/MillsAnalysis/23.gif 23
http://www.solipsys.co.uk/new/images/MillsAnalysis/24.gif 24
http://www.solipsys.co.uk/new/images/MillsAnalysis/25.gif 25
http://www.solipsys.co.uk/new/images/MillsAnalysis/26.gif 26
http://www.solipsys.co.uk/new/images/MillsAnalysis/27.gif 27
http://www.solipsys.co.uk/new/images/MillsAnalysis/28.gif 28
http://www.solipsys.co.uk/new/images/MillsAnalysis/29.gif 29
http://www.solipsys.co.uk/new/images/MillsAnalysis/30.gif 30
http://www.solipsys.co.uk/new/images/MillsAnalysis/31.gif 31
http://www.solipsys.co.uk/new/images/MillsAnalysis/32.gif 32
http://www.solipsys.co.uk/new/images/MillsAnalysis/33.gif 33
http://www.solipsys.co.uk/new/images/MillsAnalysis/34.gif 34
http://www.solipsys.co.uk/new/images/MillsAnalysis/35.gif 35
http://www.solipsys.co.uk/new/images/MillsAnalysis/36.gif 36
http://www.solipsys.co.uk/new/images/MillsAnalysis/37.gif 37
http://www.solipsys.co.uk/new/images/MillsAnalysis/38.gif 38
http://www.solipsys.co.uk/new/images/MillsAnalysis/39.gif 39
http://www.solipsys.co.uk/new/images/MillsAnalysis/40.gif 40
http://www.solipsys.co.uk/new/images/MillsAnalysis/41.gif 41
http://www.solipsys.co.uk/new/images/MillsAnalysis/42.gif 42
http://www.solipsys.co.uk/new/images/MillsAnalysis/43.gif 43
http://www.solipsys.co.uk/new/images/MillsAnalysis/44.gif 44
http://www.solipsys.co.uk/new/images/MillsAnalysis/45.gif 45
http://www.solipsys.co.uk/new/images/MillsAnalysis/46.gif 46
http://www.solipsys.co.uk/new/images/MillsAnalysis/47.gif 47