With the promise of the warmth of summer around the corner and countless varieties of flowers blooming from the once-cold ground, spring’s beauty is endlessly captivating. Flowers are beacons of color, present all around, beckoning creatures to explore them. Their colors can range from the most saturated of reds, to the quietest baby blues, with everything in between. It’s no surprise that flowers have been an inspiration to artists for hundreds of years. Every flower is a new experience, a new system, a new world.

Math is found all around us in nature. Flowers are the most popular example of the evidence of mathematical structures in nature and an embodiment of the ever presence of mathematical phenomena. The shapes of their petals can be defined with parametric equations and the placement of florets around a central axis can be defined with the golden ratio.

Did flowers and plants first discover math?

᠃ ⚘᠂ ⚘ ˚ ⚘ ᠂ ⚘ ᠃

This is a study of the colors, forms, and patterns of 3D parametric flowers.

By creating flowers that may not exist, but could exist, this is an index of what’s possible and a nod at what’s to come.

᠃ ⚘᠂ ⚘ ˚ ⚘ ᠂ ⚘ ᠃

Debug settings / keybinds

The most up-to-date version of Google Chrome is the recommended browser to view this project (other Chromium browsers work too)


Press Z to change lighting direction, camera target, to save a screenshot of the canvas, or to render a high res PNG

Camera position can be changed with a mouse click, camera target can be moved using keys Q, E, W, A, S, D (see keybinds menu for details “K”)

Ridiculously large images can be exported from this project, up to 60,000 x 60,000 px (maybe more!) if you press Z and set the proper settings to render a high res PNG. (Warning: your computer may take a while to render this image, less samples = less time). Think of a Blender render with tiles; it works the same way. The final output composition is rendered exactly as it appears on your screen.

Press K to see a list of all keybinds

H and J only make changes on the debug screen, if debug isn’t engaged they only make changes in the first 2 seconds on the loading screen

Press F in the first 2 seconds on the loading screen to set debug options


The debug options are:

Depth of field: enable a depth of field blur (focal point can be changed by clicking in the scene)


savePngAuto: save a screenshot of canvas as a png after a certain number of samples have been rendered


transparentBG: render the piece as a transparent PNG with a transparent BG (works with high res render)


noClearBG: don’t clear pixels from the renderer, creates glitches but looks cool


bigPNGKeepBG: don’t clear pixels from the large PNG builder, same as above but can create tiled compositions on large png render

Overwrite reduction settings:

Change the mesh reduction value for certain groups of flowers (can be used to fix unexpected holes in the mesh; this is enabled by default to improve rendering performance)

High res dots: set dots to be high res, you can set a custom dot resolution (makes dot generation slower! But dots are seamlessly circular)


High res stamens: set stamens to be high res, can fix high res render issues if you zoom into a stamen

Resolution settings (flower geometry):

Change the flower geometry resolutions: can be used to make the flower meshes extremely high or low res when they’re generated. If the angularity of certain flowers impacts your viewing, I recommend changing these parameters.

Renderer pixel resolution (1:1 ratio):

Can change the canvas resolution. It’s the same for each side of the canvas. The limit of this depends on your machine and web browser’s max implementation. The most common limit I’ve found is 4096 x 4096 (use 4,000 instead).

Press C to confirm your selections