the patterns considered here, one pattern fills the whole domain. On the Sun, however, every supergranule has its individual shape. It is therefore possible that a coupling is present not only at the Fourier components with equal length ($|\bk_0|=|\bl_0|=|\bmm_0|$, as for regular hexagons), but potentially for any coupling triad of Fourier components. As a consequence, the signature in Fourier space is a more complex combination of the previous characteristics at several Fourier components. This motivates the definition of the bispectrum.

Bispectral analysis in two dimensions {#secBispectrumIntro}
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Here we introduce and summarize the definition of the bispectrum and related quantities for two-dimensional random processes. This part is mainly based on Section 11.5.1 in [@Priestley1981], [@Kim1979], and [@Chandran1990]. Later in this section, we give a few examples and illustrate the definitions with the help of the patterns introduced in the previous section. In addition, we introduce a method for generating data with a given bispectrum.

Definition of the bispectrum {#secBispecDef}
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Here we consider a random field $X(\bx)$ that depends on a two-dimensional discretely sampled spacial variable $\bx$. We assume that all statistical properties of $X(\bx)$ are translation invariant. This is the generalization of a stationary process to two (spatial) dimensions. 