Code Golf: Ulam Spiral

Answer 1

Python - 176

This one starts with a big long list of newline characters and replaces all of them except for the ones that are needed at the end of the lines.

Starting at the centre, the algorithm peeps around the lefthand corner at each step. If there is a newline character there, turn left otherwise keep going forward.

w=input()*2;v=w-1;a=['\n']*v*w;p=w/2*v-1;d=0;z=[w,-1,-w,1]
for i in range(v*v):a[p]=' *'[i and all((i+1)%f for f in range(2,i))];d=d%4-(a[p+z[d-1]]<' ');p+=z[d]
print"".join(a)

Python - 177
Using a string avoids "join" but ends up one byte longer since the string is immutable

w=input()*2;v=w-1;a='\n'*v*w;p=w/2*v-1;d=0;z=[w,-1,-w,1]
for i in range(v*v):a=a[:p]+' *'[i and all((i+1)%f for f in range(2,i))]+a[p+1:];d=d%4-(a[p+z[d-1]]<' ');p+=z[d]
print a

Answer 2

MATLAB: 182 167 156 characters

Script ulam.m:

A=1;b=ones(1,4);for i=0:(input('')-2),c=b(4);b=b+i*8+(2:2:8);A=[b(2):-1:b(1);(b(2)+1:b(3)-1)' A (b(1)-1:-1:c+1)';b(3):b(4)];end;disp(char(isprime(A)*10+32))

And formatted a little nicer:

A = 1;
b = ones(1,4);
for i = 0:(input('')-2),
  c = b(4);
  b = b+i*8+(2:2:8);
  A = [b(2):-1:b(1); (b(2)+1:b(3)-1)' A (b(1)-1:-1:c+1)'; b(3):b(4)];
end;
disp(char(isprime(A)*10+32))

Test cases:

>> ulam
2
* *
  *
*  
>> ulam
3
*   *
 * * 
*  **
 *   
  *  
>> ulam
5
    * *  
 *     * 
* *   *  
   * * * 
  *  ** *
 * *     
*   *    
 *   *   
*     *  

Answer 3

Haskell - 224 characters

(%)=zipWith(++)
r x=[x]
l 1=r[1]
l n=r[a,a-1..b]++(m r[a+1..]%l s%m r[b-1,b-2..])++r[d-s*2..d]where{d=(n*2-1)^2;b=d-s*6;a=d-s*4;s=n-1}
p[_]='*'
p _=' '
i n=p[x|x<-[2..n],n`mod`x==0]
m=map
main=interact$unlines.m(m i).l.read

i'm not the best at haskell so there is probably some more shrinkage that can occur here

output from echo 6 | runghc ulam.hs

*   *      
     * *   
* *     * *
 * *   *   
    * * *  
   *  ** * 
* * *      
 *   *     
* *   *   *
 *     *   
  *        

---

this is a different algorithm (similar to @drhirsch's) unfortunately i cannot seem to get it below 239 characters

p[_]='*'
p _=' '
main=interact$unlines.u.read
i n=p[x|x<-[2..n],n`mod`x==0]
u(n+1)=map(map(i.f.o).zip[-n..n].replicate((n+1)*2-1))[n,n-1..(-n)]
f(x,y,z)=4*y*y-x-y+1+if z then 2*(x-y)else 0
o(u,v)=if(v> -u)==(v<u)then(v,u,v<u)else(u,v,v<u)

Answer 4

Python - 171

drhirsch's C ported to python.

S=input();R=range(-S+1,S)
for w in R:
 p="";v=-w
 for u in R:d=v<u;x,y=[(u,v),(v,u)][(w>=u)^d];x=4*y*y-x-y+1+2*d*(x-y);p+=" *"[(x>1)*all(x%f for f in range(2,x))]
 print p

echo 20 |python ulam.py 
      *     *   * *   *             *  
 *     * *     *   * *                 
*     * *                     *     *  
       * *     *   *           *     * 
                  *   * *   *          
 *               *   *       *   * *   
*     *   *           * *     *        
 *   * *     * *     *     *           
* *           *           *   *     * *
   *     *   *       *     *           
    *   *         *   * *   * * *      
 * *       *     *         * *   *     
      *     *   * *               *    
                   * *     *   *   * * 
*   *   *   * *   *       *   * *      
                   * *   *             
  *       *   * *     * * *     * * *  
   * * * * * * * *   *       *         
                  * * *           *    
             *   *  ** * * *   * * *   
      *       * * *                    
               *   *                   
    *   * *   * *   *   * *   *   * *  
 *     *   *   *     *     * *   *     
                *           *          
 *         * *     *   *   *       * * 
* *     *   *           *       *     *
   *     *     *   * *                 
              * *   *     *   *     *  
   * * * *         * *     *     * *   
      *   *           * *              
 *   * *     *     *   * *           * 
  * *       *         *       *     *  
             * *   * *         *     * 
          *   *     *     *         * *
       * *     *                 *     
*   *       *           *   *     *    
                             *     *   
*   * *   *     *           *          

Answer 5

Lua, 302 characters

s=...t={" "}n=2 function p()for j=2,n-1 do if n%j==0 then n=n+1 return" "end
end n=n+1 return"*"end for i=2,s do for k=#t,1,-1 do t[k+1]=t[k]..p()end
t[1]=""for k=1,i*2-1 do t[1]=p()..t[1]end for k=2,#t do t[k]=p()..t[k]end
t[#t+1]=""for k=1,i*2-1 do t[#t]=t[#t]..p()end end print(table.concat(t,"\n"))

Output from lua ulam.lua 6:

*   *      
     * *   
* *     * *
 * *   *   
    * * *  
   *  ** * 
* * *      
 *   *     
* *   *   *
 *     *   
  *        

Answer 6

Ruby 1.8.7, 194 chars

n=2*gets.to_i-1
r=n**2
l,c=[nil]*r,r/2
r.times{|i|l[c]=i+1;c=i==0||l[c-n]&&!l[c+1]?c+1:l[c-1]&&!l[c-n]?c-n:l[c+n]?c-1:c+n}
r.times{|i|print"1"*l[i]!~/^1?$|^(11+?)\1+$/?'*':' ',i%n==n-1?"\n":''}

For some reason, ruby1.9 wants another space on line 4:

r.times{|i|l[c]=i+1;c=i==0||l[c-n]&&!l[c+1]?c+1:l[c-1]&&!l[c-n]?c-n :l[c+n]?c-1:c+n}