Chemical synthesis typically yields the most thermodynamically stable ordered arrangement, a principle also governing surface synthesis on an atomically level two-dimensional (2D) surface, fostering the creation of structured 2D formations. The linear connection arising from energetically stable chemical bonding precludes the generation of a 2D random network comprised of one-dimensional (1D) convoluted stripes through on-surface synthesis. Nonetheless, we underscored that on-surface synthesis possesses the capability not solely to fashion a 2D ordered linear network but also to fabricate a winding 2D network employing a precursor with a soft ring and intermediate state bonding within the Ullmann reaction. Here, on-surface synthesis was exhibited on Cu(111) employing a 2D self-assembled monolayer array of 4,4',5,5'-tetrabromodibenzo[18]crown-6 ether (BrCR) precursors. These precursors were purposefully structured, with a crown ether ring at the core and Br atoms positioned at the head and tail ends, facilitating preferential connections along the elongated axis to foster a 1D stripe configuration. We illustrate how adjustments in the quantities of the intermediate state, serving as a primary linkage, can yield a labyrinthine, convoluted winding 2D network of stripes. The progression of growth, underlying mechanisms, and electronic structures were scrutinized using an ultrahigh vacuum low-temperature scanning tunneling microscopy and spectroscopy (STM/STS) setup combined with density functional theory (DFT) calculations. This experimental evidence opens a novel functionality in leveraging on-surface synthesis for the formation of a 2D random network. This discovery holds promise as a pioneering constituent in the construction of a ring host supramolecule, augmenting its capability to ensnare guest atoms, molecules, or ions.