'Complexity implies design and therefore creation' is basically the creationist's point. 'How can all this (usually indicating a natural phenomenon that inspires awe or an organism that appears particular well suited to its environment) have come about by chance it must be design?'

 

To unpick this question requires a more than superficial understanding of what we mean by complexity, design and chance.

 

Think of chance and one thinks of throwing a couple of dice and extrapolates this to 'let's throw atoms into the air and isn't it unlikely that they fall into a complex pattern like an animal?' Thinking of chance on a human timescale is not comparable to a spacetime scale of 13 billion years and 100 billion light years.  It requires a good grasp of non-intuitive probability theory to really understand this.

 

Think of design and we have a person labouring away over schematics putting bits together - a watchmaker.

 

Our only understanding of creation and design is an evolutionary process. No human designed thing springs fully formed from the mind. We are inspired by things we see, we manipulate the environment we try things out, we modify sometimes over generations of use and gradually design improves. Our understanding of design is much more like evolution than it is like spontaneous creation. Creation and design are simply misnomers; they give the appearance of explaining something when in fact they do not.

 

Complexity: we have nothing to compare anything to. Every element of the universe is complex to a degree beyond our understanding. Since everything is complex we have nothing to compare degrees of complexity to. Thus it is meaningless to assert that complexity is an indicator of anything.  

 

We regard things as complex because we can't understand and duplicate them. Why should we be able to and why does our failing imply anything? As technology progresses we regard more things as comprehensible. A computer with its software would be unfathomably complex to a person of a 100 years ago. The human genome was incomprehensibly complex fifty years ago. We progress, complexity unwinds.