“To appreciate the nature of fractals, recall Galileo's splendid manifesto that "Philosophy is written in the language of mathematics and its characters are triangles, circles and other geometric figures, without which one wanders about in a dark labyrinth." Observe that circles, ellipses, and parabolas are very smooth shapes and that a triangle has a small number of points of irregularity. Galileo was absolutely right to assert that in science those shapes are necessary. But they have turned out not to be sufficient, "merely" because most of the world is of infinitely great roughness and complexity. However, the infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales.”

From Italian: La filosofia è scritta in questo grandissimo libro, che continuamente ci sta aperto innanzi agli occhi (io dico l'Universo), ma non si può intendere, se prima non il sapere a intender la lingua, e conoscer i caratteri ne quali è scritto. Egli è scritto in lingua matematica, e i caratteri son triangoli, cerchi ed altre figure geometriche, senza i quali mezzi è impossibile intenderne umanamente parola; senza questi è un aggirarsi vanamente per un oscuro labirinto.
Other translations:
Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.
The Assayer (1623), as translated by Thomas Salusbury (1661), p. 178, as quoted in The Metaphysical Foundations of Modern Science (2003) by Edwin Arthur Burtt, p. 75.
Philosophy is written in this grand book — I mean the universe — which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in a dark labyrinth.
As translated in The Philosophy of the Sixteenth and Seventeenth Centuries (1966) by Richard Henry Popkin, p. 65
Il Saggiatore (1623)
Source: Galilei, Galileo. Il Saggiatore: Nel Quale Con Bilancia Efquifita E Giufta Si Ponderano Le Cofe Contenute Nellalibra Astronomica E Filosofica Di Lotario Sarsi Sigensano, Scritto in Forma Di Lettera All'Illustr. Et Rever. Mons. D. Virginio Cesarini. In Roma: G. Mascardi, 1623. Google Play. Google. Web. 22 Dec. 2015. <https://play.google.com/store/books/details?id=-U0ZAAAAYAAJ>.