The Drosophila blastoderm embryo undergoes rapid cycles of nuclear division. This poses a challenge to genes that need to reliably sense the concentrations of morphogen molecules to form desired expression patterns. Here we investigate whether the transcriptional state of hunchback (hb), a target gene directly activated by the morphogenetic protein Bicoid (Bcd), exhibits properties indicative of inheritance between mitotic cycles. To achieve this, we build a dataset of hb transcriptional states at the resolution of individual nuclei in embryos at early cycle 14. We perform a spatial point pattern (SPP) analysis to evaluate the spatial relationships among the nuclei that have distinct numbers of hb gene copies undergoing active transcription in snapshots of embryos. Our statistical tests and simulation studies reveal properties of dispersed clustering for nuclei with both or neither copies of hb undergoing active transcription. Modeling of nuclear lineages from cycle 11 to cycle 14 suggests that these two types of nuclei can achieve spatial clustering when, and only when, the transcriptional states are allowed to propagate between mitotic cycles. Our results are consistent with the possibility where the positional information encoded by the Bcd morphogen gradient may not need to be decoded de novo at all mitotic cycles in the Drosophila blastoderm embryo.