list3 = NestList[ ArrayFlatten[{{{#, 0, #}, {0, 0, 0}, {#, 0, #}}, {{0, 0, 0}, {0, #, 0}, {0, 0, 0}}, {{#, 0, #}, {0, 0, 0}, {#, 0, #}}}] &, {{{1}}}, 3];
How can the code form in the image be rewritten equivalently in one-dimensional form?
You forgot the ,3 at the end of ArrayFlatten:
,3
ArrayFlatten
NestList[ArrayFlatten[{ {{#, 0, #}, {0, 0, 0}, {#, 0, #}}, {{0, 0, 0}, {0, #, 0}, {0, 0, 0}}, {{#, 0, #}, {0, 0, 0}, {#, 0, #}}}, 3] &, {{{1}}}, 3]