can you name anyone from history who has done such researches on this?
Leonardo da Vinci
History
Leonardo da Vinci 
what does patterns in nature refer to? They are visible regularities of form found in the natural world. what patterns does it include? It includes symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. what is it caused by? Causes can be in the mathematics that governs what patterns can physically form, and among living things in the effects of natural selection, that govern how patterns evolve. were these indicated in any books? UNANSWERABLE
Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. Pythagoras, Empedocles, Plato, Theophrastus etc Pythagoras, Empedocles to  A. H. Church, and D'Arcy Thompson.
Patterns in nature Patterns in nature Patterns in nature
Introduction History History
. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.

In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. T Pythagoras Early Greek philosophers attempted to explain order in nature, anticipating modern concepts. Pythagoras (c. 570–c. 495 BC) explained patterns in nature like the harmonies of music as arising from number, which he took to be the basic constituent of existence. Empedocles (c. 494–c. 434 BC) to an extent anticipated Darwin's evolutionary explanation for the structures of organisms. Plato (c. 427–c. 347 BC) argued for the existence of natural universals. He considered these to consist of ideal forms ( "eidos": "form") of which physical objects are never more than imperfect copies. Thus, a flower may be roughly circular, but it is never a perfect circle.

Theophrastus (c. 372–c. 287 BC) noted that plants "that have flat leaves have them in a regular series"; Pliny the Elder (23–79 AD) noted their patterned circular arrangement. Centuries later, Leonardo da Vinci (1452–1519) noted the spiral arrangement of leaf patterns, that tree trunks gain successive rings as they age, and proposed a rule
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Patterns in nature [SEP] History
Theophrastus (c. 372–c. 287 BC) noted that plants "that have flat leaves have them in a regular series"; Pliny the Elder (23–79 AD) noted their patterned circular arrangement. Centuries later, Leonardo da Vinci (1452–1519) noted the spiral arrangement of leaf patterns, that tree trunks gain successive rings as they age, and proposed a rule purportedly satisfied by the cross-sectional areas of tree-branches. Johannes Kepler (1571–1630) pointed out the presence of the Fibonacci sequence in nature, using it to explain the pentagonal form of some flowers. In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series.