Square, diamond, square, diamond

Question

Task

Given a non-empty string of lowercase ASCII letters a-z, take its first character, and:

• Surround it with a square of copies of the second character,
• Surround that with a diamond of copies of the third character,
• Surround that with a square of copies of the fourth character…

…alternating between square and diamond borders until the end of the string. Empty space between the borders should be represented by ASCII spaces ().

To add a square border, draw a square exactly around the entire current “working array”:

                                               sssssssssss
                                t              s    t    s
                               t t             s   t t   s
                              t   t            s  t   t  s
                             t aaa t           s t aaa t s
                            t  aca  t    =>    st  aca  ts
                             t aaa t           s t aaa t s
                              t   t            s  t   t  s
                               t t             s   t t   s
                                t              s    t    s
                                               sssssssssss

To add a diamond border, draw a centered diamond shape that touches the outermost square diagonally, but not orthogonally:

                                                     s            
                                                    s s           
                                                   s   s          
                                                  s     s         
                                                 s       s        
                                                s         s       
                                               s           s      
                    wwwwwwwwwww               s wwwwwwwwwww s     
                    w    o    w              s  w    o    w  s    
                    w   o o   w             s   w   o o   w   s   
                    w  o   o  w            s    w  o   o  w    s  
                    w o eee o w           s     w o eee o w     s 
                    wo  eme  ow    =>    s      wo  eme  ow      s
                    w o eee o w           s     w o eee o w     s 
                    w  o   o  w            s    w  o   o  w    s  
                    w   o o   w             s   w   o o   w   s   
                    w    o    w              s  w    o    w  s    
                    wwwwwwwwwww               s wwwwwwwwwww s     
                                               s           s      
                                                s         s       
                                                 s       s        
                                                  s     s         
                                                   s   s          
                                                    s s           
                                                     s            

Your program must output the final array.

• Each line may contain any amount of trailing spaces.
• You may output a list of strings representing lines, or a single newline-separated string with an optional trailing newline.
• Leading/trailing blank lines are disallowed.
• Leading columns of spaces are also disallowed.

This is code-golf. The shortest code in bytes wins.

Test cases

The above examples are expected outputs for cat, cats, meow, and meows, in reading order. Some other cases worth handling:

• For the input a, your program should output:

  a
  

• For the input ab, your program should output:

  bbb
  bab
  bbb
  

• For the input codegolf, your program should output:

  fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
  f                            l                            f
  f                           l l                           f
  f                          l   l                          f
  f                         l     l                         f
  f                        l       l                        f
  f                       l         l                       f
  f                      l           l                      f
  f                     l             l                     f
  f                    l               l                    f
  f                   l                 l                   f
  f                  l                   l                  f
  f                 l                     l                 f
  f                l                       l                f
  f               l                         l               f
  f              l                           l              f
  f             l ooooooooooooooooooooooooooo l             f
  f            l  o            g            o  l            f
  f           l   o           g g           o   l           f
  f          l    o          g   g          o    l          f
  f         l     o         g     g         o     l         f
  f        l      o        g       g        o      l        f
  f       l       o       g         g       o       l       f
  f      l        o      g           g      o        l      f
  f     l         o     g eeeeeeeeeee g     o         l     f
  f    l          o    g  e    d    e  g    o          l    f
  f   l           o   g   e   d d   e   g   o           l   f
  f  l            o  g    e  d   d  e    g  o            l  f
  f l             o g     e d ooo d e     g o             l f
  fl              og      ed  oco  de      go              lf
  f l             o g     e d ooo d e     g o             l f
  f  l            o  g    e  d   d  e    g  o            l  f
  f   l           o   g   e   d d   e   g   o           l   f
  f    l          o    g  e    d    e  g    o          l    f
  f     l         o     g eeeeeeeeeee g     o         l     f
  f      l        o      g           g      o        l      f
  f       l       o       g         g       o       l       f
  f        l      o        g       g        o      l        f
  f         l     o         g     g         o     l         f
  f          l    o          g   g          o    l          f
  f           l   o           g g           o   l           f
  f            l  o            g            o  l            f
  f             l ooooooooooooooooooooooooooo l             f
  f              l                           l              f
  f               l                         l               f
  f                l                       l                f
  f                 l                     l                 f
  f                  l                   l                  f
  f                   l                 l                   f
  f                    l               l                    f
  f                     l             l                     f
  f                      l           l                      f
  f                       l         l                       f
  f                        l       l                        f
  f                         l     l                         f
  f                          l   l                          f
  f                           l l                           f
  f                            l                            f
  fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
  

Reference implementation

I wrote some Julia code that your program’s output should match (at least visually). Try it online!

Answer 1

JavaScript (ES6), 294 288 287 284 256 246 240 238 220 bytes

My first golf on this site. Pass input string to function f, e.g. f('codegolf')

f=s=>{N=n=>(2<<n/2+.5)-3-n%2
D=N(l=s.length)
for(a=[],i=S=D*2+1;i--;)a[i]=a[S+~i]=Array(S).fill` `
for(;l--;)for(o=n=N(l+1),I=0;I<=n;I++,o-=~l&1)a[y=D+I][x=D+o]=a[x][y]=a[y][D-o]=a[x][D-I]=s[l]
return a.map(r=>r.join``)}

-6 bytes thanks to @Sunny Pun: Remove parentheses when passing template strings.

-2 bytes thanks to @ETHproductions: Change S-i-1 to S+~i, l%2||o-- to o-=~l&1.

-18 bytes per suggestions of @Sunny Pun, @edc65: Remove prompt() and console.log() in favor of function format, don't .join() final array of strings

Answer 2

Haskell, 138 137 136 bytes

q 1=0
q x=(mod x 2+1)*(q(x-1)+1)
f x|m<-q$length x,n<-abs<$>[-m..m]=[do j<-n;max" "[c|(k,c)<-zip[1..]x,cycle[max i j,i+j]!!k==q k]|i<-n]

Defines a function f which returns the result as a list of lines

-1 byte thanks to @Lynn

Answer 3

C++ - 373 366 362 359 bytes

-1 by @TuukkaX, -6 by @Kevin Cruijssen, -4 by imports, -3 by @Baum mit Augen

#import<string>
#import<vector>
#define A(x) abs(x-r)
using S=std::string;using V=std::vector<S>;int R(int n){return n?(n%2)?R(n-1)+1:2*R(n-1)+2:0;}V f(S w){int l=w.size(),r=R(l-1),s=r*2+1,i,j,k;V x(s);for(i=0;i<s;++i){x[i]=S(s,46);for(j=0;j<s;++j)for(k=0;k<l;++k){if(A(i)<=R(k)&A(j)<=R(k)&k%2?A(i)==R(k)|A(j)==R(k):(A(i)+A(j)==R(k)))x[i][j]=w[k];}}return x;}

http://ideone.com/5y54mx

Note: This solution uses the dot ('.') as "space" character to make the empty spaces more visible. To use a space instead, one has to change S(s,46) to S(s,32). The score remains the same.

Ungolfed:

#import<string>
#import<vector>

#define A(x) abs(x-r) //r will be the center coordinate

using S=std::string;
using V=std::vector<S>;

int R(int n){ //recursive function returning the radius of a square/diamond
    return n?  //if(n!=0)
        (n%2)? //if(n%2 != 0)
            R(n-1)+1 //square -> just increase radius by 1
        :
            2*R(n-1)+2 //diamond -> radius doubles + 2
    :
        0 //n==0 -> end of recursion
    ;
}

V f(S w){ //function taking a string and returning a vector<string>
    int l=w.size(),r=R(l-1),s=r*2+1,i,j,k;  //r is radius (==center coord), s is size
    V x(s);  //vector<string>
    for(i=0;i<s;++i){  //loop over vector
        x[i]=S(s,46); //initialize string with dots. use 32 for spaces
        for(j=0;j<s;++j)
            for(k=0;k<l;++k){ //loop over word
                if(
                    A(i)<=R(k) //check bounds
                    &
                    A(j)<=R(k)
                    &
                    k%2?A(i)==R(k)|A(j)==R(k):(A(i)+A(j)==R(k))
                    //for square: check if distance to center of one coordinate = R
                    //for diamond: check if sum of distances = R
                )
                    x[i][j]=w[k]; //if any is true, replace default char
            }
    }

    return x;
}

Try ungolfed online

How to use:

include<iostream>

void printSquare(std::string word){
    auto result = f(word);
    for(auto& s:result)
        std::cout << s << std::endl;
    std::cout << std::endl << std::endl;
}

int main() {
    printSquare("a");
    printSquare("ab");
    printSquare("cat");
    printSquare("cats");
    printSquare("meow");
    printSquare("meows");
    printSquare("codegolf");
    return 0;
}

Output:

a


bbb
bab
bbb


....t....
...t.t...
..t...t..
.t.aaa.t.
t..aca..t
.t.aaa.t.
..t...t..
...t.t...
....t....


sssssssssss
s....t....s
s...t.t...s
s..t...t..s
s.t.aaa.t.s
st..aca..ts
s.t.aaa.t.s
s..t...t..s
s...t.t...s
s....t....s
sssssssssss


wwwwwwwwwww
w....o....w
w...o.o...w
w..o...o..w
w.o.eee.o.w
wo..eme..ow
w.o.eee.o.w
w..o...o..w
w...o.o...w
w....o....w
wwwwwwwwwww


............s............
...........s.s...........
..........s...s..........
.........s.....s.........
........s.......s........
.......s.........s.......
......s...........s......
.....s.wwwwwwwwwww.s.....
....s..w....o....w..s....
...s...w...o.o...w...s...
..s....w..o...o..w....s..
.s.....w.o.eee.o.w.....s.
s......wo..eme..ow......s
.s.....w.o.eee.o.w.....s.
..s....w..o...o..w....s..
...s...w...o.o...w...s...
....s..w....o....w..s....
.....s.wwwwwwwwwww.s.....
......s...........s......
.......s.........s.......
........s.......s........
.........s.....s.........
..........s...s..........
...........s.s...........
............s............


fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
f............................l............................f
f...........................l.l...........................f
f..........................l...l..........................f
f.........................l.....l.........................f
f........................l.......l........................f
f.......................l.........l.......................f
f......................l...........l......................f
f.....................l.............l.....................f
f....................l...............l....................f
f...................l.................l...................f
f..................l...................l..................f
f.................l.....................l.................f
f................l.......................l................f
f...............l.........................l...............f
f..............l...........................l..............f
f.............l.ooooooooooooooooooooooooooo.l.............f
f............l..o............g............o..l............f
f...........l...o...........g.g...........o...l...........f
f..........l....o..........g...g..........o....l..........f
f.........l.....o.........g.....g.........o.....l.........f
f........l......o........g.......g........o......l........f
f.......l.......o.......g.........g.......o.......l.......f
f......l........o......g...........g......o........l......f
f.....l.........o.....g.eeeeeeeeeee.g.....o.........l.....f
f....l..........o....g..e....d....e..g....o..........l....f
f...l...........o...g...e...d.d...e...g...o...........l...f
f..l............o..g....e..d...d..e....g..o............l..f
f.l.............o.g.....e.d.ooo.d.e.....g.o.............l.f
fl..............og......ed..oco..de......go..............lf
f.l.............o.g.....e.d.ooo.d.e.....g.o.............l.f
f..l............o..g....e..d...d..e....g..o............l..f
f...l...........o...g...e...d.d...e...g...o...........l...f
f....l..........o....g..e....d....e..g....o..........l....f
f.....l.........o.....g.eeeeeeeeeee.g.....o.........l.....f
f......l........o......g...........g......o........l......f
f.......l.......o.......g.........g.......o.......l.......f
f........l......o........g.......g........o......l........f
f.........l.....o.........g.....g.........o.....l.........f
f..........l....o..........g...g..........o....l..........f
f...........l...o...........g.g...........o...l...........f
f............l..o............g............o..l............f
f.............l.ooooooooooooooooooooooooooo.l.............f
f..............l...........................l..............f
f...............l.........................l...............f
f................l.......................l................f
f.................l.....................l.................f
f..................l...................l..................f
f...................l.................l...................f
f....................l...............l....................f
f.....................l.............l.....................f
f......................l...........l......................f
f.......................l.........l.......................f
f........................l.......l........................f
f.........................l.....l.........................f
f..........................l...l..........................f
f...........................l.l...........................f
f............................l............................f
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff


+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+............................................................+............................................................+
+...........................................................+.+...........................................................+
+..........................................................+...+..........................................................+
+.........................................................+.....+.........................................................+
+........................................................+.......+........................................................+
+.......................................................+.........+.......................................................+
+......................................................+...........+......................................................+
+.....................................................+.............+.....................................................+
+....................................................+...............+....................................................+
+...................................................+.................+...................................................+
+..................................................+...................+..................................................+
+.................................................+.....................+.................................................+
+................................................+.......................+................................................+
+...............................................+.........................+...............................................+
+..............................................+...........................+..............................................+
+.............................................+.............................+.............................................+
+............................................+...............................+............................................+
+...........................................+.................................+...........................................+
+..........................................+...................................+..........................................+
+.........................................+.....................................+.........................................+
+........................................+.......................................+........................................+
+.......................................+.........................................+.......................................+
+......................................+...........................................+......................................+
+.....................................+.............................................+.....................................+
+....................................+...............................................+....................................+
+...................................+.................................................+...................................+
+..................................+...................................................+..................................+
+.................................+.....................................................+.................................+
+................................+.......................................................+................................+
+...............................+.........................................................+...............................+
+..............................+...........................................................+..............................+
+.............................+.CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC.+.............................+
+............................+..C............................r............................C..+............................+
+...........................+...C...........................r.r...........................C...+...........................+
+..........................+....C..........................r...r..........................C....+..........................+
+.........................+.....C.........................r.....r.........................C.....+.........................+
+........................+......C........................r.......r........................C......+........................+
+.......................+.......C.......................r.........r.......................C.......+.......................+
+......................+........C......................r...........r......................C........+......................+
+.....................+.........C.....................r.............r.....................C.........+.....................+
+....................+..........C....................r...............r....................C..........+....................+
+...................+...........C...................r.................r...................C...........+...................+
+..................+............C..................r...................r..................C............+..................+
+.................+.............C.................r.....................r.................C.............+.................+
+................+..............C................r.......................r................C..............+................+
+...............+...............C...............r.........................r...............C...............+...............+
+..............+................C..............r...........................r..............C................+..............+
+.............+.................C.............r.ooooooooooooooooooooooooooo.r.............C.................+.............+
+............+..................C............r..o............F............o..r............C..................+............+
+...........+...................C...........r...o...........F.F...........o...r...........C...................+...........+
+..........+....................C..........r....o..........F...F..........o....r..........C....................+..........+
+.........+.....................C.........r.....o.........F.....F.........o.....r.........C.....................+.........+
+........+......................C........r......o........F.......F........o......r........C......................+........+
+.......+.......................C.......r.......o.......F.........F.......o.......r.......C.......................+.......+
+......+........................C......r........o......F...........F......o........r......C........................+......+
+.....+.........................C.....r.........o.....F.eeeeeeeeeee.F.....o.........r.....C.........................+.....+
+....+..........................C....r..........o....F..e....t....e..F....o..........r....C..........................+....+
+...+...........................C...r...........o...F...e...t.t...e...F...o...........r...C...........................+...+
+..+............................C..r............o..F....e..t...t..e....F..o............r..C............................+..+
+.+.............................C.r.............o.F.....e.t.ooo.t.e.....F.o.............r.C.............................+.+
++..............................Cr..............oF......et..oVo..te......Fo..............rC..............................++
+.+.............................C.r.............o.F.....e.t.ooo.t.e.....F.o.............r.C.............................+.+
+..+............................C..r............o..F....e..t...t..e....F..o............r..C............................+..+
+...+...........................C...r...........o...F...e...t.t...e...F...o...........r...C...........................+...+
+....+..........................C....r..........o....F..e....t....e..F....o..........r....C..........................+....+
+.....+.........................C.....r.........o.....F.eeeeeeeeeee.F.....o.........r.....C.........................+.....+
+......+........................C......r........o......F...........F......o........r......C........................+......+
+.......+.......................C.......r.......o.......F.........F.......o.......r.......C.......................+.......+
+........+......................C........r......o........F.......F........o......r........C......................+........+
+.........+.....................C.........r.....o.........F.....F.........o.....r.........C.....................+.........+
+..........+....................C..........r....o..........F...F..........o....r..........C....................+..........+
+...........+...................C...........r...o...........F.F...........o...r...........C...................+...........+
+............+..................C............r..o............F............o..r............C..................+............+
+.............+.................C.............r.ooooooooooooooooooooooooooo.r.............C.................+.............+
+..............+................C..............r...........................r..............C................+..............+
+...............+...............C...............r.........................r...............C...............+...............+
+................+..............C................r.......................r................C..............+................+
+.................+.............C.................r.....................r.................C.............+.................+
+..................+............C..................r...................r..................C............+..................+
+...................+...........C...................r.................r...................C...........+...................+
+....................+..........C....................r...............r....................C..........+....................+
+.....................+.........C.....................r.............r.....................C.........+.....................+
+......................+........C......................r...........r......................C........+......................+
+.......................+.......C.......................r.........r.......................C.......+.......................+
+........................+......C........................r.......r........................C......+........................+
+.........................+.....C.........................r.....r.........................C.....+.........................+
+..........................+....C..........................r...r..........................C....+..........................+
+...........................+...C...........................r.r...........................C...+...........................+
+............................+..C............................r............................C..+............................+
+.............................+.CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC.+.............................+
+..............................+...........................................................+..............................+
+...............................+.........................................................+...............................+
+................................+.......................................................+................................+
+.................................+.....................................................+.................................+
+..................................+...................................................+..................................+
+...................................+.................................................+...................................+
+....................................+...............................................+....................................+
+.....................................+.............................................+.....................................+
+......................................+...........................................+......................................+
+.......................................+.........................................+.......................................+
+........................................+.......................................+........................................+
+.........................................+.....................................+.........................................+
+..........................................+...................................+..........................................+
+...........................................+.................................+...........................................+
+............................................+...............................+............................................+
+.............................................+.............................+.............................................+
+..............................................+...........................+..............................................+
+...............................................+.........................+...............................................+
+................................................+.......................+................................................+
+.................................................+.....................+.................................................+
+..................................................+...................+..................................................+
+...................................................+.................+...................................................+
+....................................................+...............+....................................................+
+.....................................................+.............+.....................................................+
+......................................................+...........+......................................................+
+.......................................................+.........+.......................................................+
+........................................................+.......+........................................................+
+.........................................................+.....+.........................................................+
+..........................................................+...+..........................................................+
+...........................................................+.+...........................................................+
+............................................................+............................................................+
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Answer 4

MATL, 63 54 bytes

l&)"X@o?TT@I$Ya}t&n2/Xkw2+-|thYa9Mqt_w&:|&+tleXM=@*+]c

Try it Online!

Explanation

            % Implicitly grab the input as a string
l&)         % Separate the first letter from the rest and push them onto the stack
"           % For every letter in the string besides the first
  X@o?      % If this is an odd iteration through the loop
    TT      % Push the array [1, 1]
    @       % Get current character
    I$Ya    % Pad the matrix with 1 copy of this character on all sides
  }         % Else (this is a diamond)
    t       % Duplicate the matrix
    &n      % Determine the number of rows and columns (push separately to stack)
    2/Xk    % Compute the radius (half the # of columns rounded up)
    w2+     % Flip the stack to get the # of rows and add 2. This is the new radius.
    -|      % Subtract the new and old radii and take the absolute value
    thYa    % Apply the necessary number of padding zeros to the matrix
    9Mqt_w&:% Generate the array [-radius ... 0 ... radius]
    |&+     % Take the absolute value and compute the element-wise sum with itself
            % and automatically broadcast to a matrix. For a radius of 5 this yields
            % the following:
            %
            %   8   7   6   5   4   5   6   7   8
            %   7   6   5   4   3   4   5   6   7
            %   6   5   4   3   2   3   4   5   6
            %   5   4   3   2   1   2   3   4   5
            %   4   3   2   1   0   1   2   3   4
            %   5   4   3   2   1   2   3   4   5
            %   6   5   4   3   2   3   4   5   6
            %   7   6   5   4   3   4   5   6   7
            %   8   7   6   5   4   5   6   7   8
            % 
    tleXM   % Duplicate and compute the mode of this matrix (4 in the example above)
    =@*     % Find the locations where the matrix is equal to the mode and
            % replace with the current character. Set all else to 0.
    +       % Add this to the padded version of the previous iteration. 
 ]          % End of if...else
 c          % Cast the current matrix as a character array (zeros are spaces)
            % Implicit end of for loop and implicit display 
    

Answer 5

Mathematica, 167 bytes

Grid@Fold[g=Normal@SparseArray[h=f;a_List/;Plus@@Abs[a-#-1]==#->#3,2{#,#}+1]+a[#2,#/2+1]&[Length@#+1,#,#2]&;h=f=(h=g;a=ArrayPad)[#,1,#2]&;h@##&,{{#}},{##2}]/.Rule[0,]&

The input must be a list of characters.

e.g.

Grid@Fold[ ... ]/.Rule[0,]&["i","n","p","u","t"]

Answer 6

JavaScript (ES6), 252 bytes

f=([c,...r],a,n,d)=>c?a?d?f(r,[...Array(m=n+n+3)].map((_,i,b)=>b.map((_,j)=>(a[i-g]||[])[j-g]||(i+j-h&&j+h-i&&h+i-j&&i+j-h*3?` `:c)),h=m>>1,g=m-n>>1),m,0):f(r,[b=[...a].fill(c),...a,b].map(b=>[c,...b,c]),n+2,1):f(r,[[c]],1,0):a.map(b=>b.join``).join`\n`

<input oninput=o.textContent=this.value&&f(this.value)><pre id=o>

Where \n represents the literal newline character.

Answer 7

JavaScript (ES6), 204 229 238

An anonymous function returning an array of strings

s=>[...s].map(v=>{T=(x,y)=>((r=[...c[y+z]||' '.repeat(z+z)])[z+x]=r[z-x]=v,c[z+y]=c[z-y]=r.join``);for(y=o-~o,o*=++i%2+1;y--;i%2?T(q,y):T(o,q,T(q,o)))q=y-o;++o},l=s.length,z=(2<<-~l/2)-3-l%2,c=[i=o=0])&&c

Less golfed

s=>(
  l = s.length,
  z = (2 << l/2 + .5) - 3 - l%2, // zero position, total width and height are z+z+1
  c = [], // output canvas
  o = 0, // base drawing offset from z
  [...s].map( (v, i) => {
    // execute for each char v at position i in input string
    // helper function to put current char v at position (z+y, z+x),(z+y,z-x),(z-y,z+x),(z-y,z-x)
    // as the image has vertical and horizontal symmetry
    T=(x,y) =>(
      r = [...c[y+z]||' '.repeat(z+z)]), // convert string to array to set char at given pos
      r[z+x] = v, 
      r[z-x] = v,
      c[z+y] = c[z-y] = r.join`` // array to string again
    ); 
    // shorter than if(i%2) {for ...}else{for ...}
    // o is doubled at every other step
    //   and incremented (below) at each step
    for(y=o+o, i % 2 ? 0 : o=o*2; y >= 0; y--)
      q = y-o,
      i % 2 // even and odd steps have different shapes
        ? ( T(o,q), T(q,o))
        : T(q,y);
    ++o 
  }),
  c
)

Test

f=
s=>[...s].map(v=>{T=(x,y)=>((r=[...c[y+z]||' '.repeat(z+z)])[z+x]=r[z-x]=v,c[z+y]=c[z-y]=r.join``);for(y=o-~o,o*=++i%2+1;y--;i%2?T(q,y):T(o,q,T(q,o)))q=y-o;++o},l=s.length,z=(2<<-~l/2)-3-l%2,c=[i=o=0])&&c

function update()
{
  O.textContent=f(I.value).join`\n`
}

update()

<input id=I value=CodeGolf oninput='update()'>
<pre id=O></pre>

Answer 8

Java - 429 417 bytes

int r,l;int D(int n){return Math.abs(n-r);}int R(int n){return n=(n!=0)?((n%2!=0)?(R(n-1)+1):(2*R(n-1))+2):n;}char[][]C(String a){char[]c=a.toCharArray();l=a.length();r=R(l-1);int s=r*2+1,i,j,k;char[][]x=new char[s][s];for(i=0;i<s;i++){for(j=0;j<s;j++){x[i][j]=' ';for(k=0;k<l;k++){if(D(i)<=R(k)&&D(j)<=R(k)){if(k%2!=0){if(D(i)==R(k)||D(j)==R(k)){x[i][j]=c[k];}}else{if(D(i)+D(j)==R(k)){x[i][j]=c[k];}}}}}}return x;}

Credit goes to @Anedar as it was an influence on the structure of this answer

Ungolfed:

int r, l;

int D(int n) {
    return Math.abs(n - r);
}

int R(int n) {
    return n = (n != 0) ? ((n % 2 != 0) ? (R(n - 1) + 1) : (2 * R(n - 1)) + 2) : n;
}

char[][] C(String a) {
    char[] c = a.toCharArray();
    l = a.length();
    r = R(l - 1);
    int s = r * 2 + 1, i, j, k;
    char[][] x = new char[s][s];
    for (i = 0; i < s; i++) {
        for (j = 0; j < s; j++) {
            x[i][j] = ' ';
            for (k = 0; k < l; k++) {
                if (D(i) <= R(k) && D(j) <= R(k)) {
                    if (k % 2 != 0) {
                        if (D(i) == R(k) || D(j) == R(k)) {
                            x[i][j] = c[k];
                        }
                    } else if (D(i) + D(j) == R(k)) {
                        x[i][j] = c[k];
                    }
                }
            }
        }
    }
    return x;
}

Answer 9

JavaScript (ES6), 322 bytes

Non Competitive

var L=s=>{var A=Array,a,D,c,d=-1,i,k,w,O,Z,P=(u,v)=>{Z=O-(d>>1);a[D?u-v+O:u+Z][D?u+v+O-d+1:v+Z]=c},G=(c,i)=>(D=~i&1)?(d+=2,w=2*d-1):(d+=d+1,w=d);s=[...s];s.map(G);a=A(w).fill(0).map(a=>A(w).fill` `);O=w>>1;d=-1;s.map((C,i)=>{G(0,i);c=C;for(k=d;k--;)P(0,k),P(d-1,k),P(k,0),P(k,d-1)});return a.map(v=>v.join("")).join("\n")}

Less Golphed

var L=s=>{
    var A=Array,a,D,c,d=-1,i,k,w,O,Z
    P=(u,v)=>{
        Z=O-(d>>1)
        a[D?u-v+O:u+Z][D?u+v+O-d+1:v+Z]=c},
    G=(c,i)=>(D=~i&1)?(d+=2,w=2*d-1):(d+=d+1,w=d)
    s=[...s]
    s.map(G)
    a=A(w).fill(0).map( a=>A(w).fill` `)
    O=w>>1
    d=-1
    s.map((C,i)=>{
        G(0,i)
        c=C
        for(k=d;k--;)
            P(0,k),P(d-1,k),P(k,0),P(k,d-1)})
    return a.map(v=>v.join("")).join("\n")
}

Test with

L("arty*")

Easy gains by leaving out the leading var L= and .join("\n") in the return statement for -17 bytes, but type them back in to test the code :D

It's a two pass answer, evaluating the width (w) required to plot a square or diamond plot, before plotting points with P in the second pass using rotation and translation. d is the dimension (height or width) of an unrotated square before translation or rotation.

Rotation and scale by √2 details from Mathematica answer. Use of tagged string template from first answer in this thread. Thanks to both for the learning. Votes for the question and answers.

Answer 10

Powershell, 269 245 238 bytes

$m,$a=$args
if($a){$a|%{$c=$_
$w=$m[0].Length
$m=&({$i=0
($m|%{$_+'.'*$w+'.'})+(0..$w|%{'..'*$w+'.'})|%{($s=$_|% t*y)[--$i]=$c
-join$s}},{$m|%{$_+$c}
$c*$w+$c})[++$k%2]}
$m=($w=$m[0].Length-1)..1+0..$w|%{$m[$_]|%{-join($_[$w..1]+$_)}}}
$m

Ungolfed, explained & test scripted:

$f={

# $args is input char array
# $m is canvas.
# This script draws a right-bottom quadrant (axes included) on the canvas.
# If $args contains one char only then $m contains this char and whole image at same time.
$m,$a=$args                             # $a is other chars array
if($a){
    $a|%{
        $c=$_                           # $c is current char
        $w=$m[0].Length                 # $w is width of the canvas
        $m=&({                          # $m is the result of executing one of the two scriptblocks
            # draw Diamond quadrant
            $i=0
            ($m|%{$_+'.'*$w+'.'})+      # expand the canvas
            (0..$w|%{'..'*$w+'.'})|%{   # add new lines
                ($s=$_|% t*y)[--$i]=$c  # take a diamond edge on each line of the canvas
                -join$s
            }
        },{
            # draw Square quadrant
            $m|%{$_+$c}                 # expand the canvas
            $c*$w+$c                    # add new line
        })[++$k%2]                      # get a scriptblock from the array and execute it
    }

    # We have a right-bottom part of drawn AsciiArt now. Flip, flip, paste it.
    $w=$m[0].Length-1                   # width of the canvas
    $m=$w..1+0..$w|%{$m[$_]|%{          # flip vertical
        -join($_[$w..1]+$_)             # flip horizontal
    }}
}
$m

}

@(
,('c',@"
c
"@)
,('ca',@"
aaa
aca
aaa
"@)
,('cat',@"
....t....
...t.t...
..t...t..
.t.aaa.t.
t..aca..t
.t.aaa.t.
..t...t..
...t.t...
....t....
"@)
,('cats',@"
sssssssssss
s....t....s
s...t.t...s
s..t...t..s
s.t.aaa.t.s
st..aca..ts
s.t.aaa.t.s
s..t...t..s
s...t.t...s
s....t....s
sssssssssss
"@)
,('meows',@"
............s............
...........s.s...........
..........s...s..........
.........s.....s.........
........s.......s........
.......s.........s.......
......s...........s......
.....s.wwwwwwwwwww.s.....
....s..w....o....w..s....
...s...w...o.o...w...s...
..s....w..o...o..w....s..
.s.....w.o.eee.o.w.....s.
s......wo..eme..ow......s
.s.....w.o.eee.o.w.....s.
..s....w..o...o..w....s..
...s...w...o.o...w...s...
....s..w....o....w..s....
.....s.wwwwwwwwwww.s.....
......s...........s......
.......s.........s.......
........s.......s........
.........s.....s.........
..........s...s..........
...........s.s...........
............s............
"@)
,('codegolf',@"
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
f............................l............................f
f...........................l.l...........................f
f..........................l...l..........................f
f.........................l.....l.........................f
f........................l.......l........................f
f.......................l.........l.......................f
f......................l...........l......................f
f.....................l.............l.....................f
f....................l...............l....................f
f...................l.................l...................f
f..................l...................l..................f
f.................l.....................l.................f
f................l.......................l................f
f...............l.........................l...............f
f..............l...........................l..............f
f.............l.ooooooooooooooooooooooooooo.l.............f
f............l..o............g............o..l............f
f...........l...o...........g.g...........o...l...........f
f..........l....o..........g...g..........o....l..........f
f.........l.....o.........g.....g.........o.....l.........f
f........l......o........g.......g........o......l........f
f.......l.......o.......g.........g.......o.......l.......f
f......l........o......g...........g......o........l......f
f.....l.........o.....g.eeeeeeeeeee.g.....o.........l.....f
f....l..........o....g..e....d....e..g....o..........l....f
f...l...........o...g...e...d.d...e...g...o...........l...f
f..l............o..g....e..d...d..e....g..o............l..f
f.l.............o.g.....e.d.ooo.d.e.....g.o.............l.f
fl..............og......ed..oco..de......go..............lf
f.l.............o.g.....e.d.ooo.d.e.....g.o.............l.f
f..l............o..g....e..d...d..e....g..o............l..f
f...l...........o...g...e...d.d...e...g...o...........l...f
f....l..........o....g..e....d....e..g....o..........l....f
f.....l.........o.....g.eeeeeeeeeee.g.....o.........l.....f
f......l........o......g...........g......o........l......f
f.......l.......o.......g.........g.......o.......l.......f
f........l......o........g.......g........o......l........f
f.........l.....o.........g.....g.........o.....l.........f
f..........l....o..........g...g..........o....l..........f
f...........l...o...........g.g...........o...l...........f
f............l..o............g............o..l............f
f.............l.ooooooooooooooooooooooooooo.l.............f
f..............l...........................l..............f
f...............l.........................l...............f
f................l.......................l................f
f.................l.....................l.................f
f..................l...................l..................f
f...................l.................l...................f
f....................l...............l....................f
f.....................l.............l.....................f
f......................l...........l......................f
f.......................l.........l.......................f
f........................l.......l........................f
f.........................l.....l.........................f
f..........................l...l..........................f
f...........................l.l...........................f
f............................l............................f
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
"@)
#,('codegolfes',"")
) | % {
    $s, $e = $_
    $c = $s-split''-ne''
    $r = &$f @c
    $r = $r-join"`n"
    "$($e-eq$r): $s`n$r"
}