We can define a new Hash in a smart way by using Hash#new and passing it a block:

h = Hash.new {|hash,key| hash[key] = hash[key-1] + hash[key-2]} h[1] = 0 h[2] = 1 puts h[3] #=> 1 puts h[100] #=> 218922995834555169026

Here an example of famous Collatz Conjecture:

h = Hash.new {|hash,n| hash[n] = 1 + (n.odd? ? hash[3*n+1] : hash[n/2])} h[1] = 1 puts h[100] #=> 26 puts h[1000] #=> 112

via: thoughbot’s blog