SPDE-Visuals
Image Collection
This folder contains a variety of images, most of which were generated using MidJourney (denoted by the prefix MJ or my username on discord chenle02). The file names are based on the prompts used for generating the images. Below is an organized breakdown of the images by their themes and purposes. These images were used in some of my past talks.
Stochastic Heat Equation (SHE)
These images are visual representations or interpretations of the stochastic heat equation (SHE), parabolic Anderson model, etc. :
- chenle02_Stochastic_heat_equation.png
- chenle02_Chaotic_stochastic_heat_flow_on_a_torus.png
- chenle02_Intermittency_parabolic_Anderson_model_Brownian_motion.png
- MJ_SHE.png
- MJ_SHE_Sphere.png
- MJ_SHE_Torus.png
The following images are used to show my favorite initial condition: the Dirac delta initial data.
The following examples illustrate intermittency and are taken from Zeldovich’s book Almighty Chances:
- chenle02_Mushrooms_in_clusters_in_a_forest_with_sun_shades_ultr.png
- chenle02_In_a_dense_forest_there_is_a_folk_where_two_roads_dive_fbb81936-8ba4-41b4-af9a-5872d385313d.png
- MJ_Mushroooms_Forest.png
- MJ_Mushroooms_Forest_4pics.png
Cosmic and Universe Themes
Exploring cosmic forces, the universe, and other celestial concepts:
- chenle02_A_person_in_front_of_the_whole_universe_gallaxies.png
- chenle02_Cosmic_forces_beyond_comprehension.png
- chenle02_Was_it_nuclear_explosionor_cosmic_forces_beyond_comprehension.png
- chenle02_A_homesick_guy_looking_back_to_Earch_from_Mars_cinemar.png
- chenle02_Standing_on_the_planet_Mars_looking_at_home_the_earth.png
- chenle02_Imagine_a_massive_object_such_as_a_black_hole_or_neutr_335e7ef3-5235-4cda-8233-f3feb9eac5c5.png
- MJ_Curious_person_Facing_Universe1.png
- MJ_Curious_person_Facing_Universe2.png
- MJ_Evolution_Universe_4pics.png
Natural and Environmental Themes
Nature-inspired images, including forests, mushrooms, and lightning:
- chenle02_Show_rain_drops_on_a_small_pond_in_a_foggy_raining_day.png
- chenle02_Lightningclouds_dramatic_light_zigzag_highly_detailed.png
- MJ_Folk_in_Forest.png
- MJ_Folk_in_Forest_more_realistic.png
- MJ_Growing_Snow_Sufface.png
Mathematical and Theoretical Concepts
Visualizations inspired by mathematical ideas and models:
- chenle02_Law_of_large_numbers_and_central_limit_theorem.png
- chenle02_Demonstrate_the_turbulent_chaotic_stochastic_heat_flow_1a0001f2-80fa-4f5f-bdec-4127c89b326d.png
- MJ_Chaos_Intermittency_SPDEs1.png
- MJ_Chaos_Intermittency_SPDEs2.png
- MJ_SWE_Chaos_Propogation.png
Examples of Stochastic Wave Equation
The following is an example from Walsh’s 1986 notes, which describes a one-dimensional stochastic wave equation—the vibration of a guitar string in a sandstorm:
Usage
These images can be used for academic purposes, presentations, and creative projects. If you use these images, proper attribution to the repository and respective tools (e.g., MidJourney for MJ images) is appreciated.
For further exploration and downloads, visit the repository: SPDE-Visuals Repository.