Julia, 66 chars
x="print(\"x=\$(repr(x))\\n\$x;\"^2);";print";print("x=$(repr(x))\n$x"^2\n$x;"^2)
Output (134 chars):
x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);
Result of executing the result (268 chars):
x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;;
next result (536 chars):
x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;x="print;x="print(\"x=\$(repr(x))\\n\$x;\"^2);""
print("x=$(repr(x))\n$x;"^2);;;
Next result (1072 chars):
x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);x="print(\"x=\$(repr(x))\\n\$x;\"^2)"
print("x=$(repr(x))\n$x;"^2);
I hope this is according to the rules.
It produces larger output, and the output itself is valid source code that produces larger output again.