The notion of recurrent fractal interpolation functions (RFIFs) was introduced by Barnsley et al. [‘Recurrent iterated function systems’, Constr. Approx.5 (1989), 362–378]. Roughly speaking, the graph of an RFIF is the invariant set of a recurrent iterated function system on $\mathbb {R}^2$ . We generalise the definition of RFIFs so that iterated functions in the recurrent system need not be contractive with respect to the first variable. We obtain the box dimensions of all self-affine RFIFs in this general setting.

中文翻译：

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一般递归分形插值函数的存在性和盒维数

Barnsley 引入了循环分形插值函数 (RFIF) 的概念等。['循环迭代函数系统'，构造。大约。5(1989), 362–378]。粗略地说，RFIF 的图是循环迭代函数系统的不变集$\mathbb {R}^2$. 我们概括了 RFIF 的定义，以便循环系统中的迭代函数不需要相对于第一个变量是收缩的。我们在此一般设置中获得了所有自仿射 RFIF 的框尺寸。