Map Art Islands: I quantified the threshold for "centeredness" so you don't have to

Discussion in 'Discussion' started by *Slagomizer*, Apr 3, 2023.

  1. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Hello all,

    There is no prefix on this post because applies to both economy and survival versions of the game.

    This post is for you if you have considered building a mapart island and wish to know exactly how "centered" an original 99x99 island must be in order for a 149x149 expansion to be sufficient for the 128x128 space a map depicts, and are curious about what "near a whole number" means in the calculations previously recommended in other posts.

    Premise:
    I'm a simp and I wanted to make a mapart of GaroldGarcia and I. Everyone seems to hate commissions (though Novembree offered, ily!!) and I think it would feel more special if I did it myself.

    I looked on the forums here and on the Googs to find information about calculating a map's bounds. You will find information in the forum here about the following:

    Spawn in on the original center of an island, on the bedrock, and press f3 to view the coordinates. Divide the X-coordinate by 128 and jot down the result. Divide the Z-coordinate by 128 and jot down the result. Each number should separately be "very" close to a whole number if the island is going to work for a mapart island.

    Huh? What does "very" mean, I asked? Very close to a whole number is not a very quantitative statement. I had heard from a buddy that he had thought very was very enough and wasted grass / money on an expansion, only to find it was a block off! ouch! So I made sure to calculate, re-check, and verify, and am now posting here so you don't have to do the same. And don't waste your resources like poor Artz___ ...

    Method:
    I made an alt. "Her" island division of coordinates was closer to 0.50 than a whole number, so I scrapped it and replaced. Next iteration, each coordinate came out with a decimal of .9375. Hmm, that's close to a whole number, but is it close enough such that I only need to acquire a 149x149 expansion rather than a 199x199 expansion? Let's see:

    When I checked with a map, I appeared to have a 4-block tolerance on the hypothetical border of a 149x149 island centered at my humble spawnpoint. This seems about the minimum one would want: if you wish to preserve resources when clearing a completed mapart, you don't want broken items spewing into the void. A four block margin on the side of the mapart space seems sufficient (it's larger on the opposite side, plenty of space for storage and for redstone contraptions to auto-flush carpet, or whathaveyou)

    1 divided by 128 = 0.0078125
    8 divided by 128 = 0.0625, the remainder I got when calculating my alt's island spawn coordinates in both the x and z directions. Four block tolerance, therefore, on the short side.

    Conclusions:
    If you wish to build a mapart island anew, and are tediously cycling through new islands to find one centered, and you don't want to waste time and resources making and using maps (four iron ingots, redstone, paper, etc... also time!!!) to verify close-calls, and don't want to goof it and spend resources on an expansion only to find it is one block off, ensure that when you divide the center coordinates of your original 99x99 island that the decimal in each direction is a whole number +/- 0.0625. This will give you a little margin so you don't void mapart blocks and a bit of tolerance for building. If you're feeling daring and wish to cut it closer, a 0.0859375 margin will be the absolute maximum you should permit. Do not expand an island for which the center x **OR** z coordinates yield a decimal remainder larger than this. You will subsequently need a 199x199 expansion, not just a 149x149 expansion, if you do that.

    Please ping me if you need help verifying your island will work and please comment if you would like clarification on the details here.

    Love and hugs,
    Slag
     
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  2. luka
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    luka macdondalds Moderator Premium

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    so much maths and brains :mindblown:

    such a proo
     
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  3. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Thanks, Luka! I think I'm finding my forums "role" as SkyBlock math nerd... I really do all these things for my own benefit, and hope to fill gaps in collective knowledge where I can identify them! I hope they help others :)
     
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  4. Dearss
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    Dearss Active Member

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    Thank you for the post slag, found it very useful.:)
     
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  5. Magik
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    Magik Well-Known Member

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    Dumb question here: Can any island be turned into a mapart island with a max expansion?
     
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  6. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Nope, not necessarily. Islands would need to be expandable to a bit larger than 199x199 to guarantee that. This can quite easily happen:

    upload_2023-4-4_11-8-27.jpeg
     
  7. KhalDrogo
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    KhalDrogo Experienced Member

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    Using Slagomizer's margin of 0.0859375, you will find that roughly only 3.6% of islands meet this requirement, so if you limit yourself to a 149x149 upgrade, then you might be looking for a while.

    To make this check a little easier, create an excel spreadsheet like this.
    upload_2023-4-5_16-31-55.png

    In cell A1 put Slagomizer's margin of 0.0859375
    In cell B2 put: =IF(OR(MOD(A2/128,1)<=$A$1,1-MOD(A2/128,1)<=$A$1),"YES","NO")
    In cell B3 put: =IF(OR(MOD(A3/128,1)<=$A$1,1-MOD(A3/128,1)<=$A$1),"YES","NO")

    Then just plug in the X and Z coords of your bedrock and if BOTH entries report "YES" then your island is centered and requires only a 149x149 upgrade.

    If you want to know if your island can be used for map art with a 199x199 upgrade, just replace the margin in cell A1.
    I'm haven't worked out what that is but Slagomizer might have it handy.

    Now to add a bit of logic to the maths and apply one major limiting factor.
    While using the margin of 0.0859375 will, in theory, yield a greater number of suitable islands by having the edge of the map art region on the edge of your 149x149 island, in practice, it doesn't because these islands don't exist. All islands coordinates are multiples of 200 (apart from some oddities) One such coordinate that would yield a remainder of 0.0859375 is 3211 but no island has coordinates like this. The nearest is 3200 which is dead centre of the map art area.
    So while 0.0859375 works, using Slagomizers original number of 0.0625 will work just the same.

    In fact, when dividing any multiple of 200 by 128, there are only 16 different remainders possible and only 3 of those 16 are the ones you are looking for. They are coloured in green.
    upload_2023-4-5_20-20-33.png

    So to make it incredibly simple. Take the x and z coordinates, round them to the nearest 200, divide by 128.
    If the decimal part of the result is 0, 9375 or 0625, then you have a map art island that only requires a 149x149 upgrade.
    Note that 1-0.9375 = 0.0625 so they are really the same case, just either side of the perfectly centered island.

    For completeness, I'll add the following table. Coordinates that when divided by 128 yield the remainders shown in orange are suitable if you expand your island to 199x199. Note compared to the 3.6% of islands that will work with a 149x149 island, 31.6 % of all islands will work with a 199x199 expansion.
    upload_2023-4-5_21-31-47.png

    Why didn't I just say this to begin with you ask! Because maths is freaking awesome and I wanted you to see how it makes our lives easier if we understand how to use it.
     
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    Last edited: Apr 5, 2023
  8. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Because I'm miffed you beat me to this (I have just about the same Excel setup in another window right now), I'm going be petty :hilarious: and note you made a rounding error: the chance to get an island that will work with only a 149x149 expansion is 3.5%.

    To elaborate just a bit further, at risk of beating a dead horse (but also because I already did it):

    upload_2023-4-5_14-10-8.png

    If you reset your island twenty times, you have about a 50% chance of one of them being workable with a 149x149 expansion. 75% likelihood you hit after island reset 39, and 90% likelihood is achieved once you've reset your island a whopping 65 times. Cooldown is 5min, iirc, but joining and leaving a co-op skirts this (not that I am advocating skirting something the devs probably didn't want us to do Dexuby, but it does work at present). This doesn't account for the fact that, if you reset too quickly, you may end up in the exact same island plot as before.

    Love and hugs,
    Slag
     
    Last edited: Apr 5, 2023
  9. KhalDrogo
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    KhalDrogo Experienced Member

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    No rounding error, just a lack of need to be exact, hence my figure was rough.:happy:
     

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  10. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Rough is a former mathematics teacher forgetting how to round.
     
  11. KhalDrogo
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    KhalDrogo Experienced Member

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    It was derived from a list of 100 consecutive island coords of which 19 were desirable.
    (19/100)^2 =0.0361 so it wasn’t a rounding error, I was simply aware that my sample pool was only adequate for a rough figure. :happy:
     
  12. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Oooooh see I’m glad I was (lovingly) harassing you. Could you tell me why you did that instead of just (3/16)^2? I’m not aware of the rows that islands are generated in, are they done in rows of 100 before moving to a new row?
     
  13. KhalDrogo
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    KhalDrogo Experienced Member

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    That's fine, us mathy types need to push each other for perfection.
    I did that early on, before I realised there were only 16 possible outcomes.
    Also, I suspect islands generate in an outward spiral.
     
  14. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Yo
    You could probably back-calculate that by triangulating some islands’ coords. One assumed Noob and Krissy would have a couple of the first. You can stalk the newest ones fairly easily. Etc. probably not worth it though. Does a spiral produce an asymptotic situation trending toward an equal distribution of the 16 possible remainders? Does a row-by-row generation of n columns? Are you interested in having a life outside of Excel and Minecraft? Should I stop asking questions while we can still see the light of day from the inside of the rabbit hole we’re burrowing down?
     
  15. SoySauce
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    SoySauce Active Member

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    i am so confusion but ill try to get a map art island when i got time to better understand it
     
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  16. Kittykat713
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    We just used new maps. Stood in the centre of our islands, activated a new map. and looked to see how much our island was covered in a single map. With two mains and an alt, between us we have three max size islands and two of them can be used for map art.
     
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  17. KhalDrogo
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    KhalDrogo Experienced Member

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    That's not too unusual. If new islands are generating in the correct row, then 9 out of 16 will work.
    If they are generating in the wrong row, then there could be as many as 1750 islands generated in a row, none of which are suitable.
     
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  18. Queen
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    Queen Well-Known Member

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    You mathematical geniuses astound me

    Keep up the great work
     
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  19. pringlesman35
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    pringlesman35 Well-Known Member

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    love the effort put into this, will use this since i did recently make a double island and wanted to utilize it for both a mega build and mapart however i came into 4 block issue of being just shy from the edge so this will in fact be very useful ty again for the math and effort

    side note how do i add reactions to posts here shoot me a message on discord longvire#8047, am somewhat new to these forums
     
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  20. *Slagomizer*
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    *Slagomizer* Moderator Moderator

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    Hey there!

    You get the ability to react to posts after I think 10? people react to yours... So I've added one to your comment here and you're on your way!

    I'm glad you appreciated the math stuff, glad to help. Sidenote- I wouldn't have mapart being made anywhere other people can visit (such as a joint build/mapart island you describe) as it could happen that someone pulls out a mapart purchased from you and updates every copy of that map made, essentially griefing the whole thing. Mapart islands need to be locked and away! Best of luck :)
     

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