Mandelbrot Fractal and Watchmaker theory as proof for gods existence?

[Mystical]

Are there specific observations of this scientifically?

Yes.

Snowflakes, crystalline minerals, and many others.

Here's what Intelligent Design says about those.

However, the problem is this : Such simple, basic "order" falls short of the degree to which actual "information" is highly "complex." --Instead, we see low information content in the structure of a crystal, which involves merely the bonding of the same two or three element(s) or molecule(s) over and over in a highly repetitious lineup, such as "A - A - A - A - A - A - A - A - ..." or "AB - AB - AB - AB - AB - AB - AB - AB - ..."
or a frost-crystal is a repetition of the water molecule, "H2O - H2O - H2O - H2O - H2O - H2O ..."
or a quartz-crystal is a repetition of the Silicon Dioxide molecule, "SiO2 - SiO2 - SiO2 - SiO2 - SiO2 - SiO2 - SiO2 - SiO2 ..."
These all exhibit high order, but low information content, which is because of the lack of complexity.

...Another example of "low-complexity" order, is : If we instruct a computer to print out "wrapping paper," we only need to program it with two simple commands: 1) "Print the word 'Joy' " and 2) "Do it again until the paper is filled." With this process, we end up with a high amount of order, but a low amount of information ...just like the quartz crystal. ---However, in contrast, the letters in a written message (such as in this paragraph) convey information, but they do not repeat in a predictable, periodic pattern ---no one can write a systematized "formula" or algorithm which can prescribe and specify each letter (or element) in such an informational sequence --short of writing each word out. With "informational complexity," basically the entire sequence must be written out word-for-word from beginning to end.
For another example of "unspecified complexity": If a computer program were created to spit out a long string of millions of letters and spaces in a totally random fashion --the string would be very complex, but would most probably contain no significant amount of information because it would exhibit almost totally unspecified complexity. It would also exhibit no functionality.

Thus, it is obvious that complexity by itself (without specificity and functionality) is never sufficient to constitute "information."

---HOWEVER, if a person (an intelligence) comes along and arranges the rows of previously random letters and spaces into a newly "specified" order to communicate something, they can then spell out a large amount of information, because the re-arranged letters now exhibit "specified complexity," with the purpose and function of communication.

In Summary: Without a significant amount of functional, complex, specified information (FCS Information) --as described above--, there can be no relevant discussion of Intelligent Design.

Origination of Information in Nature
DNA functions as the carrier of the informational instructions (much like letters in writing) for specifying the building of all the structures in living things, as well as the functions they carry out. Although the parts of DNA and proteins bond together using perfectly normal chemical laws and forces, there are no known laws or properties of chemistry or physics which could probably (without intelligent intervention) initially dictate, determine and produce the sequential order of the nucleotides which build functional DNA / RNA, nor produce the necessary sequential order of the amino acids to build a functional class of proteins ---in fact, we must note that it is precisely the capacity of the coding chemicals of DNA and protein to be combined in virtually any conceivable order, which makes them useful for building DNA and protein. Thus, the coding chemicals are essentially neutral with regard to their position in the sequential order.

Therefore, especially NOTE: There is nothing known in the physics or chemical properties of the coding chemicals which could initially produce the FCS information in DNA, RNA or proteins.
In other words: The sequential order of the building blocks of life (the FCS Information), which is necessary to produce a living thing, has not been shown to possibly have originated from any of the properties or laws of chemicals or physics.

Any other examples of order arriving from natural processes? Or ordered processes with a function? Or a machine being formed through natural processes?