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Radius

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Illustrations for the various radius effects explained on Editing rulesets for rectangular or isometric topologies (hex topologies are simpler and different). On this page (x,y) means (+x,+y), (-x,+y), (+x,-y), (-x,-y), or one of the four identical (y,x) distances, picking x>y if different to represent four x=y or eight x<>y +/- sign combinations.

On this page the delta column contains the value for an accumulative "squared radius" effect, if you want to get from the previous radius (x',y') to the next radius (x,y) in the order shown below, e.g., to get from (3,1) for any squared radius 3*3+1*1=10 to (3,2) for any squared radius 3*3+2*2=13 the delta is 13-10=3.

Square sums Edit

ToDo: Identify the corresponding integer sequences in the Online Encyclopedia of Integer Sequences.

 Sq. sum       Delta Tiles       ASCII art       Freeciv example
 x*x+y*y (x,y)              9876543210123456789

       0 (0,0)     0     1           o           Classic buoy

                                     *
       1 (1,0)     1     5          *o*          Cardinally adjacent
                                     *

                                    +++
       2 (1,1)     1     9          +o+          Experimental city radius
                                    +++

                                     x
                                    xxx
       4 (2,0)     2    13         xxoxx
                                    xxx
                                     x

                                    ***
                                   *****
       5 (2,1)     1    21         **o**         Classic city radius
                                   *****
                                    ***

                                   +++++
                                   +++++
       8 (2,2)     3    25         ++o++
                                   +++++
                                   +++++

                                     x
                                   xxxxx
                                   xxxxx
       9 (3,0)     1    29        xxxoxxx
                                   xxxxx
                                   xxxxx
                                     x

                                    ***
                                   *****
                                  *******
      10 (3,1)     1    37        ***o***        Experimental big city
                                  *******
                                   *****
                                    ***

                                   +++++
                                  +++++++
                                  +++++++
      13 (3,2)     3    45        +++o+++
                                  +++++++
                                  +++++++
                                   +++++

                                     x
                                   xxxxx
                                  xxxxxxx
                                  xxxxxxx
      16 (4,0)     3    49       xxxxoxxxx
                                  xxxxxxx
                                  xxxxxxx
                                   xxxxx
                                     x

                                    ***
                                   *****
                                  *******
                                 *********
      17 (4,1)     1    57       ****o****       Experimental huge city
                                 *********
                                  *******
                                   *****
                                    ***
GTK2 2.5.4 minimap test 64

16=4*4+0*0

Caveats: (4,1) for the squared radius 4*4+1*1=17 is smaller than (3,3) for 3*3+3*3=18, but (4.1) covers 57 tiles, while (3,3) covers only 49 tiles. If you want a city radius as proper subset of the (next) vision radius it won't work for city radius (4,1) with vision (3,3), because invisible tiles are also unworkable. (4,2) is the default AWACS vision radius, and you might want to stay below (4,2) for the city vision radius. The experimental ruleset uses always the same values for the city radius and the city vision; that recipe can't go wrong.
                                  +++++++
                                  +++++++
                                  +++++++
      18 (3,3)     1    49        +++o+++
                                  +++++++
                                  +++++++
                                  +++++++

                                   xxxxx
                                  xxxxxxx
                                 xxxxxxxxx
                                 xxxxxxxxx
      20 (4,2)     2    69       xxxxoxxxx        Classic AWACS vision radius
                                 xxxxxxxxx
                                 xxxxxxxxx
                                  xxxxxxx
                                   xxxxx

                                  *******
                                 *********
                                 *********
                                 *********
      25 (4,3)     5    77       ****o****
                                 *********
                                 *********
                                 *********
                                  *******
Caveats: (4,3) for the squared radius 4*4+3*3=25 is the same as (5,0) for 5*5+0*0=25, please edit this page and tell us what the server actually does for 25. And so on, (7,1) vs. (5,5) for 7*7+1*1=50=5*5+5*5, (7,4) vs. (8,1) for 7+7+4*4=85=8*8+1*1, or (8,6) vs. (10,0) for 8*8+6*6=100=10*10+0*0 are also ambiguous.
                                     +
                                  +++++++
                                 +++++++++
                                 +++++++++
                                 +++++++++
      25 (5,0)     0    81      +++++o+++++
                                 +++++++++
                                 +++++++++
                                 +++++++++
                                  +++++++
                                     +

                                    xxx
                                  xxxxxxx
                                 xxxxxxxxx
                                 xxxxxxxxx
                                xxxxxxxxxxx
      26 (5,1)     1    89      xxxxxoxxxxx
                                xxxxxxxxxxx
                                 xxxxxxxxx
                                 xxxxxxxxx
                                  xxxxxxx
                                    xxx

                                   *****
                                  *******
                                 *********
                                ***********
                                ***********
      29 (5,2)     3    97      *****o*****
                                ***********
                                ***********
                                 *********
                                  *******
                                   *****

                                 +++++++++
                                 +++++++++
                                 +++++++++
                                 +++++++++
      32 (4,4)     3    81       ++++o++++
                                 +++++++++
                                 +++++++++
                                 +++++++++
                                 +++++++++

Radius 19 Edit

Other integer values, i.e., not the sum of two squared whole numbers, are allowed. An interesting case is 19=17+2 for more than 18=3*3+3*3, but still less than 20=4*4+2*2:

 Sq. sum             Tiles       ASCII art       Freeciv example
 x*x+y*y (x,y)              9876543210123456789

                                    ***
                                   *****
                                  *******
                                 *********
      17 (4,1)          57       ****o****       Experimental huge city
                                 *********
                                  *******
                                   *****
                                    ***
 
                                  +++++++
                                  +++++++
                                  +++++++
      18 (3,3)          49        +++o+++
                                  +++++++
                                  +++++++
                                  +++++++

                                    xxx
                                  xxxxxxx
                                  xxxxxxx
                                 xxxxxxxxx
      19 (4,sqrt(3))    61       xxxxoxxxx       
                                 xxxxxxxxx
                                  xxxxxxx
                                  xxxxxxx
                                    xxx

                                   xxxxx
                                  xxxxxxx
                                 xxxxxxxxx
                                 xxxxxxxxx
      20 (4,2)          69       xxxxoxxxx        Classic AWACS vision radius
                                 xxxxxxxxx
                                 xxxxxxxxx
                                  xxxxxxx
                                   xxxxx

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