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Charles Gilman wrote on Mon, Sep 9, 2013 06:16 AM UTC:
Orbiters In my recent update of Man and Beast 09 I described how, during a single move, colourbound Curved alternators stay a constant distance from a cell not on the path (a Knight leap for the Curved Alpaca, a Camel leap for the Curved Alderney, a Zebra leap for the Curved Qualpaca, a Giraffe leap for the Curved Okalpaca, et cetera). Here is an illustration for the Curved Alpaca: 
- 0 - 7 -

1 - - - 6

- - * - -

2 - - - 5

- 3 - 4 -
I then added that colourswitching Curved alternators stay a constant distance from a position between cells (half a Camel leap for the Curved Rhino of Leaping Bat Chess, half a Zemel leap for the Curved Quagga, half a Gimel leap for the Curved Okapi, et cetera). Here is an illustration for the Curved Rhino: 
- 0 7 -

1 - - 6
   *
2 - - 5

- 3 4 -
The Curved Sprilpaca stays an Antelope's leap from a central cell, but cells a Quibbler's leap from that cell are the same distance from that central cell. This illustration shows th path of the Curved Sprilpaca and the extra cells that get added by replacing each Bitrebuchet leap with two Camel leaps to get a Fiveorbiter: 
- - - - - + - - - - -

- - 0 - - - - - 7 - -

- 1 - - - - - - - 6 -

- - - - - - - - - - -

- - - - - - - - - - -

+ - - - - * - - - - +

- - - - - - - - - - -

- - - - - - - - - - -

- 2 - - - - - - - 5 -

- - 3 - - - - - 4 - -

- - - - - + - - - - -
Likewise the Curved Springbok stays half a Namel's leap from between 4 cells, but vcells half a Quitter's leap from that cell are the same distance from that central cell. This illustration shows th path of the Curved Springbok and he extra cells added by replacing each tripper leap with two Knight leaps to get a Root12½orbiter: 
- - - 1 8 - - -

- + - - - - + -

- - - - - - - -

2 - - - - - - 7
       *
3 - - - - - - 6

- - - - - - - -

- + - - - - + -

- - - 4 5 - - -
The question is, are these mixed oblique and radial Curved movers worth considering in more depth, perhaps even adding to Man and Beast? I can also imagine orbiters at distances from central locations of the square roots of 65, 32½, 85, and 42½.

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