Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a "least action principle" which characterizes the odometer function of the growth process. Starting from an approximation for the odometer,  successively correct under- and overestimates and provably arrive at the correct final state. The degree of speedup depends on the accuracy of the initial guess.#R##N##R##N#Determining the size of the boundary fluctuations in growth models like internal diffusion-limited aggregation (IDLA) is a long-standing open problem in statistical physics. As an application of our method,  calculate the size of fluctuations over two orders of magnitude beyond previous simulations.
['Tobias Friedrich', 'Lionel Levine']
I am writing a research paper on a idea Fast simulation of large-scale growth models
[{"from": "human", "value": "I am writing a research paper on a idea Fast simulation of large-scale growth models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a \"least action principle\" which characterizes the odometer function of the growth process. Starting from an approximation for the odometer,  successively correct under- and overestimates and provably arrive at the correct final state. The degree of speedup depends on the accuracy of the initial guess.#R##N##R##N#Determining the size of the boundary fluctuations in growth models like internal diffusion-limited aggregation (IDLA) is a long-standing open problem in statistical physics. As an application of our method,  calculate the size of fluctuations over two orders of magnitude beyond previous simulations."}]