ee.List.iterate

// This example uses the ee.List.iterate function to generate a series of
// sequentially halved values.

// Declare a list that will hold the series of sequentially halved values,
// initialize it with the starting quantity.
var quantityList = [1000];

// Define the number of iterations as a list sequence.
var nSteps = ee.List.sequence(1, 10);

// Declare a function that takes the current element of the iteration list and
// the returned result of the previous iteration as inputs. In this case, the
// the function is returning an accumulating list of quantities that are reduced
// by half at each iteration.
var halfOfPrevious = function(currentElement, previousResult) {
  var previousQuantity = ee.Number(ee.List(previousResult).get(-1));
  var currentQuantity = previousQuantity.divide(2);
  return ee.List(previousResult).add(currentQuantity);
};

// Apply the function to the nSteps list, each element is an iteration.
quantityList = ee.List(nSteps.iterate(halfOfPrevious, quantityList));

// Display the results. Note that step 0 is included for the initial value.
print('Steps in the iteration of halved quantities', nSteps);
print('Series of sequentially halved quantities', quantityList);
print(ui.Chart.array.values({
  array: quantityList,
  axis: 0,
  xLabels: ee.List([0]).cat(nSteps)
}));

import matplotlib.pyplot as plt

# This example uses the ee.List.iterate function to generate a series of
# sequentially halved values.

# Declare a list that will hold the series of sequentially halved values,
# initialize it with the starting quantity.
quantity_list = [1000]

# Define the number of iterations as a list sequence.
n_steps = ee.List.sequence(1, 10)


# Declare a function that takes the current element of the iteration list and
# the returned result of the previous iteration as inputs. In this case, the
# the function is returning an accumulating list of quantities that are reduced
# by half at each iteration.
def half_of_previous(current_element, previous_result):
  previous_quantity = ee.Number(ee.List(previous_result).get(-1))
  current_quantity = previous_quantity.divide(2)
  return ee.List(previous_result).add(current_quantity)


# Apply the function to the n_steps list, each element is an iteration.
quantity_list = ee.List(n_steps.iterate(half_of_previous, quantity_list))

# Display the results.
display('Steps in the iteration of halved quantities', n_steps)
display('Series of sequentially halved quantities', quantity_list)
quantity_list_client = quantity_list.getInfo()
plt.scatter(range(len(quantity_list_client)), quantity_list_client)
plt.show()