Isometric Fractal Art Tutorial - Part 1

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By tatasz
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In this tutorial, i will explain how i created some of my recent "isometric" works. For example:

Staircase to Heaven by tatasz Surface by tatasz

Softwares needed: Apophysis and Chaotica.
Prerequisites: you will need some previous knowledge on how to use Apo and Chaotica. If you have any doubts, please check those out:

Plugins used: square.

Basic element

Start from blank, and add 1 transform with square = 1. You should have something like:

C1 by tatasz

The square above is 1x1 units, and its centered on 0,0.

Now, go to the transform tab, set it to polar and change the X angle from 0 to 30.

C2 by tatasz

This rhombus is still centered on (0,0). The length of the sides is still 1, but since it is skewed, the horizontal width is equal to sin(60) = 0.866025. Take a look at the detailed dimensions and angles below:

C3 by tatasz


About maths


Just move your post transforms by 0.25 vertically and by 0.433012 horizontally till they fit into the pattern =)
Of course understanding it could make it easier, but using the rule of the thumb above is pretty much enough to create really complicated and crazy patterns.


Making a simple cube

Now that we have the basic element and its dimensions, making a "cube" shall be easy.

Supposing this is the right face of the cube, lets now make the left face.
Duplicate transform 1.
Since the left face is a "mirrored" copy of the right one, you will need to flip the post transform.

Flip by tatasz

You see both elements will overlap: you need now to move the second one to the left, so its right edge connects with the left edge of the first element. Since the width of one rhombus is cos(60), all you need to do is to move the post transform of second transform 0.866025 left (or first transform 0.866025 right).

Move by tatasz

You should have something like this now:

First element                                                         First and second elements
C4a by tatasz C4b by tatasz

And the last part, the top face.

Again, duplicate transform 1.
The top face of our cube has same shape as its right face, but rotated 60 degrees clockwise. So rotate the post_transform 60 degrees.

Top by tatasz

It is also shifted: you can see on the picture below its center is above and to the left from the center of the right face. So shift its post transform 0.433013 left and 0.75 up.

Shift by tatasz

And the cube is ready. You can either use the logic above to create more intrincated patterns, or just use the cube as an element for tiles and other frameworks.

Cube by tatasz


About transform number

Apophysis unfortunately handles fractals with many transforms very badly, slowing down and lagging until it is almost unusable.

And, for elaborate isometric designs, you will need to use quite a lot of transforms, easily going over 30-50. Keep this in mind while designing your fractal. Some of the tips below will help you with keeping the number of transform relatively low without sacrificing a fancy design.


Tip 1 - Chaotica

Use Chaotica to render it. Makes all the difference for a pretty solid and smooth look.

Apo render:
Apo by tatasz

Chaotica render:
Black by tatasz

In Chaotica, high gamma settings work really well with this design:

Gamma by tatasz

An extra trick, set Anti-aliasing mode to Smooth.

Smooth by tatasz


Tip 2 - Bigger Elements

Re-scale the post transforms to get bigger elements instead of using several transforms.

For example, lets make a block with dimensions 1x1x2 from the cube we created above.

First, move the top face 0.5 up.
Now, go to the first transform, and change Y axis length from 1 to 2, as shown below to stretch it vertically.

2 Blocks by tatasz

And do the same for the transform 2.

You will also need to balance the weights out, since the elements are not the same size anymore. The area of the right face is now two times the area of the base element, so the weight should be multiplied by 2: since i used default weights for the base element, the new weight will be 0.5*2=1.

After stretching transforms 1 and 2, you should have something like this:

Big by tatasz


Tip 3 - Using background

For huge patterns, filling all the plane may become challenging, or just take a lot of time.

So you can just use background color to filll in the "empty" areas. I strongly recommend a Chaotica render for this, because it's the only software where this trick actually works 100% (in Apophysis, the difference between background and the tiles is visible).

Lets see, below, the same patterns with different background colors:

Black

Black by tatasz

Green
Green by tatasz

White
White by tatasz

The area that changes color was not filled with tile elements, and its color is given by the background.



Published:
© 2014 - 2020 tatasz
Comments38
anonymous's avatar
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stunam1's avatar
Excellent. How do we change the color of the planes individually? I'm in Chaotica and my cube is one color.
tatasz's avatar
go to shader. set blend speed to 1, and then play with palette location (between 0 and 1). This gives you solid color.
tatasz's avatar
=D=D those things may happen ;)
Lupsiberg's avatar
Thank you very much for sharing :iconflowerthnxplz:
Daeurth's avatar
Well haven't I missed a lot in my absence...Gonna have to give this a couple tries as soon as I can actually get Apo to install.
Lady-Compassion's avatar
Does this count as annoying? Does this count as annoying? Does this count as annoying? Does this count as annoying? Does this count as annoying? Does this count as annoying? Does this count as annoying? Does this count as annoying? !!!!!!!!!!!!!!!!!!YEA~~~~~~~
tatasz's avatar
:la: :eager: to see results
camada's avatar
OMG this tutorial is awesome. I can't wait to try this out! Thanks for this!
tatasz's avatar
:eager: for results =D
AkuraPare's avatar
very nice tutorial :) i am waiting for part two!
older one with "cubes"... Forgotten Cavern - but much simpler than your creations.
tatasz's avatar
=D well, part 2 is up, part 3 cooking =D
i mean, not really rocket science but still handy =)
ThoughtWeaver's avatar
I'm giving this a try for sure! Thank you for posting this! :D
tatasz's avatar
mozhet zamutish chto nibud'? =D
triptychaos's avatar
Taty, eu adorei, mas pensava que, depois de desenhado o cubo, um ou outro iterator faria o restante... ótima explicação!
tatasz's avatar
Bem, de uma olhada na parte 2
mas, de modo geral, qq desenho ligeiramente mais complicado e o número de iteradores vai pro espaço e tem um zilhão de artimanhas para diminuir isso (mesmo no chaotica que não fica lerdo, trabalhar com 50-100 iteradores é uma bosta porque você não sabe mais qual que é qual, mesmo botando nomes hehe)
Adrolyn's avatar
Thank you!  Now I just need to get the square plug in...
tatasz's avatar
=D grab it =)
but you can also replace it with some sinusoidal + pre_blur
anonymous's avatar
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