Exponentially Slimy Programming: Stacking Minecraft Slimes

Question

Slimes are cube shaped enemies in Minecraft that break into multiple smaller versions of themselves when killed. For the purposes of this challenge we'll depict them as an 8×8 pixel image with 3 colors:

← True 8×8 version.

The precise RGB colors are:

• 0, 0, 0 for the eyes and mouth
• 110, 170, 90 for the central, darker green
• 116, 196, 96 for the outer, lighter green

Challenge

Write a program or function that takes in a positive integer N and outputs an image of N sizes of slimes packed into a rectangle. Going from left to right, the image should follow the pattern of having:

• A stack of 2^(N-1) 8×8 slimes.
• A stack of 2^(N-2) 16×16 slimes.
• A stack of 2^(N-3) 32×32 slimes.
• And so on until the stack only contains one slime.

The slime images larger than the 8×8 version () are generated by nearest-neighbor upsampling (i.e. just doubling all the pixels). Note that you must use the exact slime design and colors given here.

The final image will contain 2^N-1 slimes and be 2^(N+3)-8 pixels wide and 2^(N+2) pixels tall.

The image may be output in any common image file format, saved to a file or printed/returned as a raw data stream, or directly displayed during runtime.

The shortest code in bytes wins.

Examples

Your program should produce these exact results.

N = 1:

N = 2:

N = 3:

N = 4:

N = 5:

N = 6:

Larger N should work just as well.

Answer 1

MATL, 77 76 74 bytes

:"')^.,9&Xze`}+.E=p'F3ZaQ8e@qWt3$Y"G@-W1X"]&h[OOO;11 17E]5*29 7U24hhE&vEYG

The code works in this commit, which is earlier than the challenge.

You can try it in MATL online. This interpreter is still experimental. If it doesn't work, try refreshing the page and pressing "Run" again.

Here's an example run in the offline interpreter:

Explanation

:                     % Input N implicitly. Generate range [1 2 ... N]
"                     % For each k in [1 2 ... N]
  ')^.,9&Xze`}+.E=p'  %   Compressed string
  F3Za                %   Decompress with target alphabet [0 1 2]
  Q                   %   Add 1
  8e                  %   Reshape into 8×8 array containing values 1, 2, 3
  @qW                 %   Push 2 raised to k-1
  t                   %   Duplicate
  3$Y"                %   Repelem: interpolate image by factor 2 raised to k-1
  G@-W                %   Push 2 raised to N-k
  1X"                 %   Repmat: repeat the array vertically. Gives a vertical strip
                      %   of repeated subimages
]                     % End for each
&h                    % Concatenate all vertical strips horizontally. This gives a big
                      % 2D array containing 1, 2, 3, which represent the three colors
[OOO;11 17E]5*        % Push array [0 0 0; 11 17 9] and multiply by 5
29 7U24hhE            % Push array [29 49 24] and multiply by 2
&vE                   % Concatenate the two arrays vertically and multiply by 2.
                      % This gives the colormap [0 0 0; 110 170 90; 116 196 96]
YG                    % Take the array and the colormap and display as an image

Answer 2

Dyalog APL, 118 113 bytes

('P3',⌽∘⍴,255,∊)(3↑(116 196 96)(110 170 90))[⊃,/i{⊃⍪/⍵⍴⊂⍺⌿⍺/8 8⍴∊22923813097005 926134669613412⊤¨⍨⊂32⍴3}¨⌽i←2*⍳⎕]

assuming ⎕IO=0

From right to left:

i←2*⍳⎕ powers 1 2 4 ... 2^n-1

i{ }¨⌽i iterate over powers (with ⍺) and reversed powers (⍵)

⊤¨⍨⊂32⍴3 decode each of the numbers on the left as 32 ternary digits

8 8⍴∊ flatten and reshape to 8×8

⍺⌿⍺/ replicate each row and column ⍺ times

⍵⍴⊂ take ⍵ copies

⊃⍪/ and stack them vertically

⊃,/ join all results horizontally

3↑(116 196 96)(110 170 90) colours; 3↑ extends them with (0 0 0)

[ ] index the colours with each element of the matrix; result is a matrix of RGBs

('P3',⌽∘⍴,255,∊) is a "train" - a function that returns 'P3' followed by the reversed shape of the argument, 255, and the argument flattened.

Answer 3

JavaScript (ES7), 326 327 bytes

n=>{x=(d=document).body.appendChild(c=d.createElement`canvas`).getContext`2d`;c.width=2*(c.height=4*(p=2**n)));for(i=0;i<n;i++){c=-1;for(j of[...'0001000001111110022112200221122011111110011121110111111000010000'])for(x.fillStyle=['#74c460','#6eaa5a','#000'][j],c++,k=0;k<p;)x.fillRect(c%8*(_=2**i)+_*8,~~(c/8)*_+_*8*k++,_,_)}}

Ungolfed ES6 Version

Try it yourself.

(n=>{
    x=(d=document).body.appendChild(c=d.createElement`canvas`).getContext`2d`;
    c.width=2*(c.height=4*(p=Math.pow(2,n)));
    for(i=0;i<n;i++){
        c=-1;
        for(j of[...'0001000001111110022112200221122011111110011121110111111000010000'])
            for(x.fillStyle=['#74c460','#6eaa5a','#000'][j],c++,k=0;k<p;)
                x.fillRect(c%8*(_=Math.pow(2,i))+_*8,~~(c/8)*_+_*8*k++,_,_)
    }
})(4);

The only difference between the ES7 and ES6 version is using ** instead of Math.pow(). You can also see, how you can invoke the function – in this example with n=4.

Result

---

Edits

• saved 1 byte - found an unnecessary trailing semicolon ;

---

^{This is pretty slow and might take some time for numbers greater 10.}

Answer 4

C, 220 bytes

x,y,r;f(n){
printf("P3 %d %d 255 ",(8<<n)-8,4<<n);
for(y=0;y<4<<n;++y)for(r=0;r<n;++r)for(x=0;x<8<<r;++x)
puts("110 170 90\0 116 196 96\0 0 0 0"+12*
(117-"` t5L\rL\ru5tst5` "[x>>r+2|(y>>r)%8*2]>>(x>>r)%4*2&3));}

I added useless newlines for readability, score is without these newlines.

Defines a function f(n) that outputs a plain PPM image on stdout.

Answer 5

Mathematica, 267 255 254 225 212 bytes

G=10{11,17,9};Image@Join[##,2]&@@Table[Join@@Table[ImageData@ImageResize[Image[{t={g=G+{6,26,6},g,g,G,g,g,g,g},f={g,a=##&[G,G,G],a,g},e={g,b=0g,b,G,G,b,b,g},e,{a,a,G,g},{g,a,b,a},f,t}/255],4*2^j],2^(#-j)],{j,#}]&

Saved 29 42 bytes thanks to Martin Ender

Golfing suggestions welcome, especially for constructing the 8 by 8 (by 3) array s. Unfortunately, there is no "ArrayResize" analogue for ImageResize, so the array needs to be converted to an image (Image) before resizing, and then back to an array (ImageData) to do the Joining.

Ungolfed:

(* dark green, light green, black *)
G = 10 {11, 17, 9};
g = G + {6, 26, 6};
b = 0 g;

(* abbreviation for triple G sequence, top row, forehead, eye level *)
a = ##&[G, G, G];
t = {g, g, g, G, g, g, g, g};
f = {g, a, a, g};
e = {g, b, b, G, G, b, b, g};

(* slime *)
s =
  {
    t,
    f,
    e,
    e,
    {a, a, G, g},
    {g, a, b, a},
    f,
    t
  }/255;

(* jth column *)
c[n_, j_] := Join @@ Table[ImageData@ImageResize[Image[s], 4*2^j], 2^(n - j)]

(* final program *)
Image@Join[##, 2] & @@ Table[c[#, j], {j, #}] &

Answer 6

Python 2.7: 424 412 405 376 357 Bytes

I'm a bit new to golfing.... here we go

from numpy import*
import PIL
def c(n,col):e=log2((col+8)/8)//1;r=2**e;t=2**(n-e-1);return tile(repeat(array([0x2df0777ca228b9c18447a6fb/3**i%3for i in range(64)],dtype=int8).reshape([8,8])[:,(col-(8*r-8))//r],r),t)
n=input();i=PIL.Image.fromarray(column_stack([c(n,col) for col in range(2**(n+3)-8)]),mode='P');i.putpalette('t\xc4`n\xaaZ'+' '*762);i.show()

ungolfed and length tested..

from numpy import*
import PIL

def c(n,col): #creates array for a given column
    s = array([0x2df0777ca228b9c18447a6fb/3**i%3for i in range(64)],dtype=int8).reshape([8,8]) #slime template (golfed inline)
    e=log2((col+8)/8)//1 #exponent for tiles and repititions
    r=2**e #number of repitions (scale factor)
    t=2**(n-e-1) #number of tiles (vertically)
    return tile(
            repeat(
             s[:,(col-(8*r-8))//r] #select appropriate column from template
              ,r) #repeat it r times
               ,t) #tile it t times

n = input()
arr = column_stack([c(n,col) for col in range(2**(n+3)-8)]) #create image array by stacking column function
i=PIL.Image.fromarray(arr,mode='P'); #colormap mode
i.putpalette('t\xc4`n\xaaZ'+' '*762); #set colormap
i.show()

s = r'''from numpy import*
import PIL
def c(n,col):e=log2((col+8)/8)//1;r=2**e;t=2**(n-e-1);return tile(repeat(array([0x2df0777ca228b9c18447a6fb/3**i%3for i in range(64)],dtype=int8).reshape([8,8])[:,(col-(8*r-8))//r],r),t)
n=input();i=PIL.Image.fromarray(column_stack([c(n,col) for col in range(2**(n+3)-8)]),mode='P');i.putpalette('t\xc4`n\xaaZ'+' '*762);i.show()'''

print len(s)

edit1: removed sys.argv[1] in favor of raw_input() to save extra import statement

edit2: shortened PIL import: removed from Image added PIL.

edit3: Thanks @Sherlock9 for the hex encode of the slime template

edit4: didn't need function def and used input() instead of raw_input()

Answer 7

R, 378 356 346 334 bytes

f=function(n){r=rep;k=r(0,4);m=r(1,6);L=c();for(i in 1:n)L=cbind(L,r(max(L,0)+2^(n-i):1,e=2^(i-1)));png(w=sum(w<-4*2^(1:n)),h=sum(h<-r(8,2^(n-1))));layout(L,w,h);for(i in 1:max(L)){par(mar=k);image(matrix(c(0,0,0,1,k,0,m,0,0,1,1,1,2,r(1,10),0,0,r(r(c(2,1,2,0),e=2),2),m,k,1,k),nr=8),col=c("#74C460","#6EAA5A",1),ax=F,an=F)};dev.off()}

Saves as a png file. Indented, with linefeeds:

f=function(n){
    r=rep
    k=r(0,4)
    m=r(1,6)
    L=c()
    for(i in 1:n)L=cbind(L,r(max(L,0)+2^(n-i):1,e=2^(i-1)))
    png(w=sum(w<-4*2^(1:n)),h=sum(h<-r(8,2^(n-1))))
    layout(L,w,h)
    for(i in 1:max(L)){
        par(mar=k)
        image(matrix(c(0,0,0,1,k,0,m,0,
                       0,1,1,1,2,r(1,10),0,
                       0,r(r(c(2,1,2,0),e=2),2),
                       m,k,1,k),
                     nr=8),
              col=c("#74C460","#6EAA5A",1),ax=F,an=F)
    }
    dev.off()
}

N=2:
N=3:
N=4:

Some explanations:

Here's the matrix that's being plotted (0 represent lightgreen, 1 darkgreen and 2 black; the matrix is tilted because columns are the y-axis and rows the x-axis):

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,]    0    0    0    1    0    0    0    0
[2,]    0    1    1    1    2    2    1    0
[3,]    0    1    1    1    2    2    1    0
[4,]    1    1    1    1    1    1    1    1
[5,]    0    1    2    1    1    1    1    0
[6,]    0    1    1    1    2    2    1    0
[7,]    0    1    1    1    2    2    1    0
[8,]    0    0    1    0    0    0    0    0

Each call to image plot that matrix (with each integer corresponding to a color). For N=4, here is L (the layout matrix, each unique number represents one single plot), w (the widths of the matrix columns) and h (the heights of the matrix rows):

> L
     [,1] [,2] [,3] [,4]
[1,]    8   12   14   15
[2,]    7   12   14   15
[3,]    6   11   14   15
[4,]    5   11   14   15
[5,]    4   10   13   15
[6,]    3   10   13   15
[7,]    2    9   13   15
[8,]    1    9   13   15
> w
[1]  8 16 32 64
> h
[1] 8 8 8 8 8 8 8 8