Science2Art, a lesson in artful prompt engineering

generative AI

prompt engineering

How can physical equations be expressed in a paintings? In the beginning I only had a few ideas and the whole process was very effortful. Then in 2023, I discovered ChatGPT. And it become a lesson in the art of prompt engineering.

Author

Dominik Lindner

Published

January 15, 2025

1 Newton’s second law of motion

\[ F = ma \]

Pushing a shopping cart with groceries, the amount of force you need to apply to get the cart moving is directly proportional to its mass and acceleration. Visible Brush Strokes Style.

2 Work-Energy theorem

\[ W = \Delta K\]

A person is lifting a box and placing it on a shelf. Communist art.

3 Gravitational force

\[ F = G * \frac{m_1 * m_2}{r^2}\]

Newtons apple, the apple falling from the tree to your hand.

4 Simple harmonic motion

\[ x = Acos(\omega t + \Phi)\]

Swinging on a swing, the back and forth motion of the swing can be described by simple harmonic motion. Impressionism Style.

5 Kinetic energy

\[ K = \frac{1}{2} m v^2\]

A foot has hit a soccer ball. Cubism art style.

6 Potential energy

\[U = mgh\]

Climbing a staircase, the higher you go, the more potential energy you have stored due to the force of gravity acting on your body. Style of Pieter Bruegel the Elder’s The Tower of Babel.

7 Elastic force

\[ F = -kx\]

Bouncing a basketball, the ball compresses and stores potential energy, which is then released and converted into kinetic energy as the ball bounces back. Surrealism style.

8 Centripetal force

\[F = m \frac{v^2}{r}\]

Riding a roller coaster, the centripetal force is what keeps you in your seat as the coaster goes around sharp turns. Neoclassicism style.

9 Moment of inertia

\[ I = m r^2\]

A ballet dancer uses the moment of inertia to speed up in turns by pulling the arms to the center. Style like Edgar Degas.

10 Momentum

\[p = m v\]

A car collision, the momentum of the cars before and after the collision can be calculated to determine the amount of force transferred between the cars. Pop Art Style.

11 Power

\[P = \frac{W}{t}\]

Using a power drill to screw in a nail, the power of the drill determines how quickly the nail is driven into the wood. Renaissance painting style.

12 Friction

\[ F_f = \mu N\]

A child slides down a slide and is keep in place by the friction.

13 Bernoulli’s equation

\[p + \frac{1}{2} \rho v^2 + \rho g h = constant\]

Feeling a decrease in air pressure as a moving car passes by, this is due to the Bernoulli’s equation as the speed of the air increases. Fauvism Style.

14 Projectile motion

\[ y = v_0 t - \frac{1}{2} g t^2\]

Throwing a ball into the air, the path it takes can be described by the equations of projectile motion. Painterly Style.

15 Torque

\[ \tau = r F\]

turning a doorknob, the force applied at a certain distance from the pivot point creates a torque. Style like Paul Cezanne.

16 Law of conservation of energy

\[\Delta E = \Delta K + \Delta U\]

A rollercoaster ride demonstrates the conservation of energy, as the potential energy of the car at the top of a hill is converted into kinetic energy as it moves downwards and vice versa.Style like Allan Rohan Crite.

17 Law of conservation of momentum

\[\frac{\delta p}{\delta t} = 0\]

In a game of pool, when a cue ball strikes another ball, the cue ball loses some of its momentum, but the momentum of the two balls before and after the collision must remain the same.

18 Hooke’s law

\[ F = -kx\]

A trampoline follows Hooke’s law as it stretches and compresses when a person jumps on it. The greater the force, the greater the stretch or compression and vice versa. Church window style.

19 Center of mass

\[ x_c = \frac{\Sigma m_ix_i}{ \Sigma m_i}\]

A scale can be used to find the center of mass of an object. If an object is placed on a scale unevenly, the scale will tip to one side until the center of mass is directly over the center of the scale. Japanese Painting.

20 Law of universal gravitation

\[ F = G \frac{ m_1 m_2}{r^2}\]

The force of attraction between the Earth and the Moon, causing the Moon to orbit the Earth, is determined by the law of universal gravitation. Neoclassicism style.

21 From idea to result

21.1 Origins

Physical phenoma are complex and often beautiful. Think about the vortex created through a bridge pillar. We can observe many physical equations in daily life. This led to the original question: How can a painting express a physical equation?.

In the beginning, I only had a few ideas, and capturing all the ideas in photos or in paintings seemed quite effortful. The entire idea landed on the pile of fancy ideas with a low effort/reward ratio.

21.2 ChatGPT & Dalle

Then in 2023 I discovered ChatGPT & Dalle. Most of the above images reflect the ChatGPT results from early 2023 and 2024.

Over the cause of time, the results of Dalle got better regarding image content. The shift from DALL-E 2 to DALL-E 3 accounts for this. See this comparison. Dalle2 vs dalle3 . To me, the Dalle3 images seem sometimes less artistic. However, they are more accurate with regard to the prompt.

21.3 The outdated art of prompt engineering

In 2023, the issue back then was to get the content correctly created regarding image content. I used prompt engineering to get ChatGPT to write correct prompts for Dalle.

I first used ChatGPT to generate equations found in daily life, along with examples. Then I used it to create prompts for Dalle. I added an art style which I found fitting for the context.

Some images required tweaking to be usable.

Nowadays, in 2025, the entire process works a lot more straightforward, but as already mentioned, all images look quite similar.

This leads to a blog post . Is prompt engineering actually something someone should learn? Or is it quickly becoming outdated by the use of AI agents?

I think it all starts with the creative process of noting your thoughts and expressing what is in your mind. If you do it on a computer or to another person, this could become very similar. For the people without the skills to craft the images themselves, it provides a better interface to the world.

21.4 Comparison 2023 vs 2024 output

I redid some images in 2024. As mentioned before, the images are smoother but have a very identical look for an identical post to the 2023 version.

2024 Version of a man with a powerdrill.

2023 Version of a man with a powerdrill.