This paper introduces a univariate interpolation scheme using a binary parameter called signature such that the graph of the interpolant—which we refer to as affine zipper fractal interpolation function—is obtained as an attractor of a suitable affine zipper. The scaling vector function is identified so that the graph of the corresponding affine zipper fractal interpolation function can be inscribed within a prescribed rectangle. Convergence analysis of the proposed affine zipper fractal interpolant is carried out. It is observed that for a fixed choice of discrete scaling factors, the box counting dimension of the graph of an affine zipper fractal interpolant is independent of the choice of a signature. Several examples of affine zipper fractal interpolants are presented to supplement our theory.

中文翻译：

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仿射拉链分形插值函数

本文介绍了一种使用称为签名的二元参数的单变量插值方案，以便获得插值图（我们将其称为仿射拉链分形插值函数）作为合适仿射拉链的吸引子。缩放向量函数被识别，以便对应的仿射拉链分形插值函数的图形可以内接在规定的矩形内。对所提出的仿射拉链分形插值进行了收敛分析。据观察，对于离散比例因子的固定选择，仿射拉链分形插值图的盒计数维数与签名的选择无关。提供了几个仿射拉链分形插值的例子来补充我们的理论。