...because you recognise a pattern (purposeful and arranged)...
You are not being very precise here. Not all patterns are purposeful or arranged. A snowflake, for example, or any other crystal has a definite pattern, yet it forms through the ordinary laws of physics as individual water molecules attach to the growing crystal.
We need some way of determining whether or not the pattern that we see on Mt. Rushmore is "purposeful" or "arranged".
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... that could not have been produced by chance.
But it's always possible to have been produced by chance. Again, you're not being very clear.
Besides that, you are discounting some natural process working in a way that I don't yet understand or recognize.
So far, you have not yet been able to figure out how to discount a natural process that we have not yet identified. Nor have we discounted the possibility, however unlikely, possibility that it occurred through chance.
If it's truly good and powerful, it deserves to engender a thousand misunderstandings. -- Ben Ratcliffe