AI-synthetic: Sanae Kichiya & Youmu Konpaku in Touhou 13 ~ Ten Desires

 

Base image: https://www.pixiv.net/en/artworks/112883314

Prompt:

The trouble some issues encountered while modelling the economic growh together with a new exponential modelling

 

The following text is AI (ChatGPT plus) generated with reference to my current issue in mathematical modelling of the macroeconomic growth theory. 

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This week I had an interesting little incident at the boundary between economics and mathematics.

I was checking an exponential model for an economic growth / Total Factor Productivity (TFP) problem. After going back to the mathematical formulation and implementing it carefully in MATLAB, the objective function $Q(\phi)$ showed a clear minimum.

At first sight, that sounds encouraging: the optimisation problem has a well-defined solution.

However, when I reconstructed the corresponding TFP trajectory using the parameters associated with that minimum, the result did not reproduce the observed trajectory satisfactorily.

So I found myself in an interesting situation:

the mathematics said, “Here is the optimum,” while the economic data replied, “Not so fast.” 😅

This does not necessarily mean that the exponential approach is mathematically wrong. Rather, it raises a more interesting question: is this particular model structure appropriate for representing the empirical behaviour of TFP?

At the moment, I am therefore also comparing the result with a penalised smoothing spline, which appears to represent the trajectory more naturally.

For me, this has been a useful reminder that finding a mathematically neat optimum is not the same thing as finding a good empirical model. Optimisation, model specification, and interpretation all have to work together.

The investigation is still ongoing, so this is not a final conclusion — just one of those small research episodes where economics and mathematics refuse to cooperate quite as politely as expected.

 

AI-synthetic: Flandre Scarlet in Remake of Touhou 6 ~ Embodiment of Scarlet Devil - Touhou Project fan-art

 

Original: https://art-blue-liberalism.blogspot.com/2026/06/flandre-scarlet-in-remake-of-touhou-6.html

pixiv: https://www.pixiv.net/en/artworks/145983809

Prompt:

AI-synthetic: Remilia, Cause against Determinism! Freedom of will shall prevail!!

 

Original: https://art-blue-liberalism.blogspot.com/2023/10/libertarian-remilia-touhou-project.html

pixiv: https://www.pixiv.net/en/artworks/112719427

Prompt:

AI-synthetic: Patchouli Knowledge — Quiet Elemental Magician in a Grand Gothic Library

 

Original image: https://www.pixiv.net/en/artworks/117812043

Prompt:  

AI-synthetic: Flandre VS Remilia

 

Original image: https://art-blue-liberalism.blogspot.com/2024/02/flandre-scarlet-with-laevatein-vs.html

pixiv: https://www.pixiv.net/en/artworks/115716194

AI-synthetic: Cirno-chan and Dai-chan, Touhou Project fan-art

 

Sorry, I'm too exhausted and preoccupied to do hand-drawing while it's still steaming hot here. Then, I'm still experimenting the AI-synthetic art with ChatGPT plus for the moment. The prompt refers to the early-20th-century British botanical fairy-book watercolour.

Original image / composition reference:
https://www.pixiv.net/en/artworks/114018549

Related original post / scene reference:
https://art-blue-liberalism.blogspot.com/2023/12/cirno-chan-and-dai-chan-touhou-project.html

Prompt  

AI synthetic: Sanae Kochiya vs Kyoko Kasodani - Touhou Project Fan-art

 

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AI Illustration Prompt — Unexpected Dawn Encounter at a Mysterious Supernatural Temple

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AI: Sanae Kochiya Vs. Mononobe No Futo in Touhou 13 ~ Ten Desires ~ Stage 5

  

AI-synthetic: Desire Drive Youmu Vs Seiga in Touhou 13

 

Original image / composition reference:
https://www.pixiv.net/en/artworks/127878750

Related original post / scene reference:
https://art-blue-liberalism.blogspot.com/2025/03/desire-drive-youmu-vs-seiga-in-touhou-13.html

Prompt:

AI synthetic Touhou fan-art: Yuyu&Myon: Yuyuko Saigyouji blocking Youmu Konpaku saying "... how irrational!" in Stage 1, Touhou 13 ~ Ten Desires ~

 

Original image / composition reference:
https://www.pixiv.net/en/artworks/128516181

Related original post / scene reference:
https://art-blue-liberalism.blogspot.com/2025/03/yuyu-yuyuko-saigyouji-blocking-youmu.html

Prompt 

Redraw this illustration while preserving the overall composition, character placement, interaction, scene layout, dramatic intent, and camera framing as closely as possible.

Use the second reference image as an expression and scene-context reference, especially for the left character’s frustrated, slightly exasperated, mildly incredulous mood.

Use the third reference image as a skin tone and skin-rendering reference, especially for the soft luminous complexion, smooth texture, gentle blush, and delicate anime-style skin shading.

Use the additional reference image of the pink-haired ghostly noblewoman as a reference for the right character’s facial design, warm illumination, skin rendering, and treatment of the surrounding ghostly wisps only, while preserving the original scene, pose, costume identity, character placement, and overall composition.

Use the small cropped reference of the left character’s original expression and torso area as an additional guide for her intended mood and general pose energy, but prioritize anatomical coherence and correct body orientation over accidental distortions in the problematic version.

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Overall Art Direction

Redraw this illustration as a polished early-to-mid-1990s Japanese fantasy RPG key illustration, reflecting the elegant visual language of Japanese fantasy strategy games, anime illustration books, and romantic shōjo-fantasy artwork from approximately 1991–1995.

The final image should combine the dramatic clarity, heroic presence, and refined fantasy atmosphere of early-1990s Japanese RPG promotional art with the graceful silhouettes, romantic colour harmony, jewel-like eyes, decorative costume design, and gentle fantasy elegance associated with period shōjo-oriented anime illustration.

Use delicate but confident linework, softly modelled cel shading, warm luminous skin tones, flowing hair with carefully separated locks, richly described fabrics, refined accessories, and a detailed atmospheric background.

Preserve the overall composition, dramatic storytelling, relative character placement, colour scheme, costume identities, signature accessories, and background concept while significantly refining the anatomy, facial expressions, line quality, costume construction, lighting, shading, and overall rendering quality.

Set the scene in a mystical Japanese ghostly mansion garden, featuring stone stairways, traditional architecture, drifting cherry blossoms, soft mist, and a dreamy supernatural atmosphere.