φ makes for good aesthetics because of its unique relationship with the number 1.

φ - 1 = 0.618 = Φ

1 / φ = 0.618 = Φ

φ² = 1 + φ = 2.618

φⁿ⁺¹ = φⁿ + φ^n-1

If thats not convincing enough, check this out:

φ = √ 1 + √1 + …

Creating designs that incorporate the golden sections replicate the chaotic harmony found in lot of nature’s design. Its only chaotic because unlike half, third etc, golden section is not visually resolvable(irrational).

The proportion however does exist and appeals to the mind making it harmonious.

The other significant reason for using golden sections in design is its repetitive nature. A canvas can be repeatedly divided into golden sections to achieve a complex but balanced design.