creatively interpreting your question, some possibilities other than GCT as you mention come to mind. one way is to look for undecidable problems (aka Turing completeness) which are quite ubiquitous.

• aperiodic Tiling the plane & Penrose tiling. its been proven that the question of whether there is an aperodic tiling of the plane is undecidable.

• Cellular automata which also increasingly are shown to have deep connections to physics, many related undecidable problems, proven TM complete, and they're naturally interpreted as (and converted between) TM computational tableaus.

• algorithms as Fractals. a more undeveloped (ie active/ongoing research!) area, but various undecidable questions, such as given a complex point $(x,y)$ is it in the Mandelbrot set?

• Undecidability in dynamical systems (Hainry), again sometimes closely connected to physics. dynamical systems generally have a multidimensional geometric interpretation.

• Visual programming languages. a program can be seen as a type of (directed?) graph with different types of vertices (eg conditional, arithmetic operation) etc.

creatively interpreting your question, some possibilities other than GCT as you mention come to mind. one way is to look for undecidable problems (aka Turing completeness) which are quite ubiquitous.

• aperiodic Tiling the plane & Penrose tiling. its been proven that the question of whether there is an aperodic tiling of the plane is undecidable.

• Cellular automata which also increasingly are shown to have deep connections to physics, many related undecidable problems, proven TM complete, and they're naturally interpreted as (and converted between) TM computational tableaus.

• algorithms as Fractals. a more undeveloped (ie active/ongoing research!) area, but various undecidable questions, such as given a complex point $(x,y)$ is it in the Mandelbrot set?

• Undecidability in dynamical systems (Hainry), again sometimes closely connected to physics. dynamical systems generally have a multidimensional geometric interpretation.

• Visual programming languages. a program can be seen as a type of (directed?) graph with different types of vertices (eg conditional, arithmetic operation) etc.

creatively interpreting your question, some possibilities other than GCT as you mention come to mind. one way is to look for undecidable problems (aka Turing completeness) which are quite ubiquitous.

• aperiodic Tiling the plane & Penrose tiling. its been proven that the question of whether there is an aperodic tiling of the plane is undecidable.

• Cellular automata which also increasingly are shown to have deep connections to physics, many related undecidable problems, proven TM complete, and they're naturally interpreted as (and converted between) TM computational tableaus.

• algorithms as Fractals. a more undeveloped (ie active/ongoing research!) area, but various undecidable questions, such as given a complex point $(x,y)$ is it in the Mandelbrot set?

creatively interpreting your question, some possibilities other than GCT as you mention come to mind. one way is to look for undecidable problems (aka Turing completeness) which are quite ubiquitous.

• aperiodic Tiling the plane & Penrose tiling. its been proven that the question of whether there is an aperodic tiling of the plane is undecidable.

• Cellular automata which also increasingly are shown to have deep connections to physics, many related undecidable problems, proven TM complete, and they're naturally interpreted as (and converted between) TM computational tableaus.

• algorithms as Fractals. a more undeveloped (ie active/ongoing research!) area, but various undecidable questions, such as given a complex point $(x,y)$ is it in the Mandelbrot set?

• Undecidability in dynamical systems (Hainry), again sometimes closely connected to physics. dynamical systems generally have a multidimensional geometric interpretation.

• Visual programming languages. a program can be seen as a type of (directed?) graph with different types of vertices (eg conditional, arithmetic operation) etc.